Workshop ‘Facets of Quantum Homogeneous Spaces’ (Room D2.01, ‘Promotie zaal’, Building D, Campus Etterbeek)

Thursday 03 December 09:00 - 09:30: Welcome 09:30 - 10:30: S. Launois 10:30 - 10:45: Coffee break 10:45 - 11:45: S. Kolb 11:45 - 13:15: Lunch break 13:15 - 14:15: J. Stokman 14:20 - 15:20: A. Mudrov ´ Buachalla 15:25 - 16:25: R. O 19:00: Dinner at restaurant ‘Les Foudres’

Friday 04 December 9:30 - 10:30: F. Bonechi 10:30 - 10:45: Coffee break 10:45 - 11:45: Y. Arano 11:45 - 13:15: Lunch break 13:15 - 14:15: P. Bieliavsky 14:20 - 15:20: S. Neshveyev 15:25 - 16:25: M. Van den Bergh

Titles and abstracts Y. Arano: Unitary representations of Drinfeld doubles Abstract: As has been observed by many authors, the Drinfeld double of the q-deformation of a compact Lie group can be regarded as a quantization of the complexification of the original Lie group. Using this point of view, I will discuss irreducible unitary representations of these Drinfeld doubles. P. Bieliavsky: 2-cocycles and symmetric spaces Abstract: TBA F. Bonechi: Quantum projective spaces from quantization of integrable models Abstract: We discuss an approach to quantum projective spaces based on the quantization of the symplectic groupoid integrating the underlying semiclassical Poisson structure. The main idea is to use the singular real polarization defined by a multiplicative integrable model, that is an integrable model compatible with the groupoid structure. The output of the construction is the groupoid of Bohr-Sommerfeld leaves and its C -algebra, that we describe explicitly. This construction is based on the bihamiltonian approach to integrable models and can be applied to other examples, like quantum grassmannians. S. Kolb: Universal K-matrix for quantum symmetric pairs Abstract: Quantum groups provide a uniform setting for solutions of the quantum Yang-Baxter equation. These solutions a realized via a universal R-matrix which lies at the heart of the origins of quantum groups in the theory of quantum integrable systems. For systems with boundary, additionally, the reflection equation enters the picture. It is expected that solutions of the reflection equation are obtained similarly via a universal K-matrix, but so far only very few examples have been constructed. The corresponding symmetry objects are realized as coideal subalgebras of quantum groups. In this talk I will give the definition of a universal K-matrix for a coideal subalgebra of a braided Hopf algebra. I will then explain how the theory of quantum symmetric pairs provides a large class of coideal subalgebras which have a universal K-matrix. The construction builds on a program of canonical bases for quantum symmetric pairs initiated by H. Bao & W. Wang and related work by M. Ehrig & C. Stroppel. The new results in this talk are joint work with

1

Martina Balagovic. S. Launois: On the quantum grassmannian Abstract: In this talk, I will discuss recent results and conjectures about the prime ideals of the quantum grassmannian, and the link with the totally nonnegative grassmannian. A. Mudrov: Representations of semi-simple quantum conjugacy classes Abstract: We discuss quantization of semi-simple conjugacy classes of simple complex groups by their representations in highest weight modules, which can be associated with every point of the maximal torus. By quantization of a variety we understand deformation of its coordinate ring and projective (one-sided) modules of global sections of vector bundles. It is assumed equivariant under the corresponding quantum group. In the established Levi case, the isotropy subgroup perfectly matches the fixed triangular decomposition of the total group, and its root basis is a part of the total basis. The quantization is encoded in the parabolic O-category and ”dynamical adjoint functor” realized via the parabolic induction. Pseudo-Levi conjugacy classes give another extreme examples when the root basis cannot be made a part of the total basis. The coordinate ring of such a class can also be quantized via highest weight modules, and there is a pseudo version of the parabolic O-category. However, there is no natural quantum isotropy subgroup and dynamical adjoint functor this time. That makes quantization of vector bundles an open problem, as well as construction of local star product. In the intermediate case of quasi-Levi initial points, the classical stabilizer is isomorphic to a Levi subalgebra but its root system is rotated with respect to the given polarization. Although the quantum stabilizor is missing as for pseudo-Levi classes, the quasi-parabolic O-category seems isomorphic to parabolic. We consider this case as a bride between Levi and non-Levi classes that may help to create a uniform quantization scheme for all semi-simple conjugacy classes. S. Neshveyev: Categorical duality for a class of Yetter-Drinfeld algebras Abstract: It is known that actions of compact quantum groups on C*-algebras can be described categorically, via weak tensor functors or module categories. In my talk I will discuss this description, as well as its refinement, which gives a correspondence between braided-commutative Yetter-Drinfeld algebras and generating tensor functors. (Based on joint work with Makoto Yamashita.)

2

´ Buachalla: The Noncommutative K¨ahler Geometry of the Full Flag Manifold of Cq rSU3 s R. O Abstract: The talk will begin by defining noncommutative complex and K¨ahler structures for differential calculi. A covariant differential calculus for Cq rF3 s, the full quantum flag manifold of Cq rSU3 s, will then be introduced, and its complex and K¨ahler structures classified. It will be shown that the dimension of the calculus and the number of classified structures are the same as in the classical case, and that the calculus restricts to the Heckenberger–Kolb calculus on Cq rCP2 s. The ring structure of the cohomology ring of the calculus will then be shown to satisfy a q-integer deformation of the classical Schubert calculus rules. Time permitting, the spectral properties of the K¨ahler–Dirac operator associated to the K¨ahler structure will be discussed. (Joint work with Petr Somberg) J. Stokman: Quantum affine symmetric pairs, affine Hecke algebras and integrable spin chains. Abstract: I will first shortly discuss the relation between integrable spin chains and quantum affine symmetric pairs. I will then turn to the dual perspective, in which appropriate quantum group intertwiners are viewed as the generators of the hidden symmetries of the integrable spin chain. In important special cases the dual symmetry structure arises as the Baxterization of an affine Hecke algebra representation. The integrable spin chain can then be analysed using the extensive theory on double affine Hecke algebras. I will explain how this leads to elliptic integrable structures by explicitly solving connection problems. M. Van den Bergh: The representation theory of noncommutative OpGLp2qq Abstract: This is about joint work with Theo Raedschelders. We discuss the universal coacting Hopf algebra for k rx, y s. We will show how the representation theory of this Hopf algebra can be studied using methods borrowed from the theory of algebraic groups.

3

Internet connection On the campus, there is connection to the eduroam network. For those without an eduroam account, there is a wifi-connection available called ‘VUBNext’. When connecting, you will have to accept a security certificate. The login and password can be found attached to the folder.

4

Area map and restaurant options On the next pages you can find maps of the area around the VUB campus which indicates some possible suggestions for going out to dinner nearby. The restaurant ‘Les foudres’ (marked ‘A’ on the map) is where the workshop dinner will take place on Thursday 03/12 at 19:00. Lunches will take place in the student restaurant (building R on the attached map). Two lunch tickets (Thursday+Friday) are included in the folder. Note that there is also the possibility to have a breakfast here (from 07:30 till 09:30). For those of you who want to go grocery shopping: on the Triomflaan, one finds a Colruyt store offering a large selection of food and drinks. They are open from Monday till Saturday between 8:30 and 20:00 (in fact, on Friday they are open till 21:00). See the included maps of the campus for the location of the Triomflaan.

5

Travel Brussels airport Brussels Airport is very well connected to the center of Brussels by rail. The train station at the airport is called “Brussel-Nat-Luchthaven/Bruxelles-Nat-Aeroport”. Timetables can be checked at http://www.belgianrail.be/. People travelling via Brussels South Charleroi Airport can get to Brussels by Brussels City Shuttle or by train. Information on how to find the trainstation, can be found at http://www.charleroiairport.com/en/acces/shuttle-buses/index.html.

Getting to the VUB The conference will be held at the VUB, Campus Etterbeek in the ”Promotie zaal”, room 2.01 in building D. The address is Pleinlaan 2, 1050 Brussel (or 1050 Elsene). Down below you can find some further information on how to reach the VUB. Getting to the VUB by train The VUB is easily accessible by train. The train station near the VUB is called ‘Etterbeek’. You can find all rail timetables at http://www.belgianrail.be/. When checking the timetables, make sure to select the station with ‘[NMBS/SNCB]’ at the end. Those are the train stations. On the next pages, you can find some further information on which train to take when travelling from “Brussel-Noord”, “Brussel-Centraal” or “Brussel-Zuid”. The Etterbeek station can also easily be reached from the train stations “Brussel-Luxemburg” and “Brussel-Schuman”. When you leave the train station, the VUB is on your right hand side. Getting to the VUB by metro The metrostations closest to the VUB are “Ptillon”, “Hankar” and “Delta”, all three situated on metroline 5. A map of the metro can be found further in this document. Getting to the VUB by tram There is also a tram station in front of the VUB, called “VUB”. This station is situated on tramlines 7 and 25.

Taxi numbers If you would need taxis for getting around in Brussels, you can opt for the following companies: • Taxis Bleus: 02 268 00 00 • Taxis Verts: 02 349 49 49 • Taxi Capital: 02 427 77 77 These phone numbers are in the format used from a local phone. If you want to dial them from an international network, use e.g. +32 2 268 00 00.

10

7

Buedts

Hansen-Soulie

Campus Etterbeek

Pétillon s ire ta on ol laan V s rs d e ige ue ill en rijw v V A

34

Pleinlaan 2 Boulevard de la Plaine 1050 Brussel - Bruxelles

Arsenal Arsenaal

!

25

Pétillon L

VUB

34

VUB Delporte

K

Stratégie Krijgskunde

Z

Comforto

Etterbeek Station / Etterbeek Gare

Bo

Y Y'

ul ev ar

M

Ch W aus av sé er e d se ste e Wa en vre we g

d m ph

e io Tr m fla an

!

Pl ain eP lei nla an

Fietspad Cycleroute 5

Hankar

la

Villo!: Fietsdelen Villo! : Bicycle sharing Cambio: Autodelen Cambio: Car sharing

!

de

Toegang Access

!

E+F+G+R B+C+D rd

Fietsuitrustingen Bicycle-park

!

!

va

Gebouwen van de ULB Buildings of the ULB Infopunt studenten Student information HUB

cq Ja an al la ér ues n G é cq rd J a va al ule nera o B Ge

ule

Parking Car-park

Bo

i

Gebouwen van de VUB Buildings of the VUB

i

T

io Tr

Legende / Legend

25

95

Etterbeek Gare s Etterbeek Station ue

!

du

Studentenhuizen

Comforto

Gewestelijke Fietsroute Regional Cycleroute

!

!

Fraiteur

!

Thys

ph

e

71

m levard72 du Trio Trio mflaa n

95

Verwezenlijkt met Brussels UrbIS Verdeling & Copyright CIBG Realized with Brussels UrbIS Distribution & Copyright CIRB

n° 112a Uitgave / Edition 06.2014 Netwerk / Network 10.03.2014

72

Triomphe Triomf

71 Bo u

Cartografie : MIVB - SMN Cartography : STIB - SMN

Delta

!

71

72 0

50

100

200

300

Cimetière d'Ixelles Begraafplaats van Elsene 400

500 m

Fig. 1: Campus Etterbeek

Michiels 17

A utoroute E411 Au tosnelweg E41 1

Vrije Universiteit Brussel Campus Etterbeek

How to get to Bereikbaarheidsfiche

Pétillon

Jonction ferroviaire Nord-Midi / Noord-Zuid spoorwegverbinding

Bruxelles-Midi Brussel-Zuid Gare du Midi Zuidstation

Bruxelles-Central Brussel-Centraal Bruxelles-Central Brussel-Centraal

2'

7' Elisabeth

Arts-Loi Kunst-Wet

IR CR

Richting Louvain la Neuve Univeristé (2 treinen / uur) to Louvain la Neuve Univeristé (2 trains / hour)

Bruxelles-Nord Brussel-Noord 2'

Gare du Nord Noordstation

-

Vrije Universiteit Brussel Campus Jette 2'

UZ Brussel

29'

5'

Etterbeek

5

7’30

6

Rogier - Boondael Gare Rogier - Boondaal Station

6

7’30

6

6

7’30

6

Stockel - Gare de l’Ouest Stokkel - Weststation

5

7’30

5

Elisabeth - Simonis

6

7’30

6

Elisabeth - Roi Baudouin Elisabeth - Koning Boudewijn

6

7’30

6

5

12

5

Bourse - Heiligenborre Beurs - Heiligenborre

Arts-Loi / Kunst-Wet

Na 20u. After 8pm

2'

5'

VUB

7’30

6

Connections Aansluitingen

11'

Simonis

1'

5

Vanderkindere - Heysel Vanderkindere - Heizel

Etterbeek Gare / Etterbeek Station

Voor 20u. Before 8pm

Boondaal Station Boondael Gare

18'

Erasme - Herrmann-Debroux Erasmus - Herrmann-Debroux

Connections Aansluitingen

Simonis-Elisabeth 8'

7' Met de trein By train

±23'

18'

29'

Koning Boudewijn Roi Baudouin

4'

12'

Pétillon

Gare Centrale Centraal Station

±29'

±33'

5'

14'

Connections Aansluitingen

1'

Arts-Loi Kunst-Wet

Brussels Airport

4'

UZ Brussel - Gare du Nord UZ Brussel - Noordstation

PM = Ochtendspits / Morning peak C = Daluren / Off-peak PS = Avondspits / Evening peak

7'

15' 10'

Dichtsbijzijnde stations: Nearest stations:

Etterbeek

4'

Boulevard Général Jacques Generaal Jacqueslaan 1040 Bruxelles / Brussel

15'

5'

VUB

Reisweg Itinerary

1 ±28'

Bruxelles-Nord Brussel-Noord

14'

Gare Centrale Centraal Station

14' 2'

IR CR

Richting Louvain la Neuve Univeristé (2 treinen / uur) to Louvain la Neuve Univeristé (2 trains / hour)

Etterbeek

Parking for transit to public transportation: CERIA, Kraainem, Delta, Herrmann-Debroux, Roodebeek, Stalle, Reyers Free parking: on campus. Er is een fietspunt op Triomflaan 40 De VUB ligt langs verschillende GFR (Gewestelijke fietsroutes). Zie reisweg op het plan. Meer informatie op de website www.mobielbrussel.irisnet.be

10' A new bicycle service point has opened nearby campus (address: Triomflaan 40). The VUB is connected to the regional cycle network See several routes on map More information on the website www.bruxellesmobilite.irisnet.be

Jette Gare Jette Station

15'

5'

5'

L

Richting / to Eigenbrakel / Braine-L’Alleud (1 train / uur) / (1 train / hour)

10'

Fraiteur

02 528 28 28 www.sncb.be www.nmbs.be

P

Het is mogelijk een taxi te nemen aan de stations Brussel-Centraal en Brussel-Zuid en aan Brussel-Noord.

Jette Etterbeek

2 ±37'

17' 2'

-

25'

Reisweg Itinerary

26'

TAXI

Dichtsbijzijnde station: Nearest station: Avenue Nouvelle 191 Nieuwlaan 1040 Bruxelles / Brussel

1 ±43'

Laerbeek-UZ Brussel Laarbeek-UZ Brussel

Every trains to Brussels

Arsenaal / Arsenal

070 23 2000 www.stib.be www.mivb.be

2' Reisweg Itinerary

Alle treinen richting Brussel

Overstapparking: COOVI, Kraainem, Delta, Herrmann-Debroux, Roodebeek, Stalle, Reyers Gratis: Ter plaats aan de VUB.

12'

Pétillon Bruxelles Nat. Aéroport Brussel Nat. Luchthaven

5'

Pétillon

Boulevard louis Schmidtlaan 2 1040 Bruxelles / Brussel

Maximum wachttijd Maximum waiting time

25'

12'

5'

Etterbeek

Met de trein By train

±37'

010 23 53 53 www.infotec.be

30'

7'

Reisweg Itinerary

2 ±38'

070 220 200 www.delijn.be

Fig. 2: How to get to Campus Etterbeek

Taxis are available at the train stations Brussel-Centraal, Brussel-Zuid and Brussel-Noord.

16'

26'

12'

Komende van Meiser / Montgomery, links voorsorteren op Louis Schmidtlaan, de Triomflaan oprijden, toegang 6. Komende van Terkamerenbos via de Generaal Jacqueslaan, na station Etterbeek, rechtsaf op de Pleinlaan, neem toegang 11 of 13. Coming from Meiser / Montgomery, get in the left lane on Louis Schmidtlaan, turn left on Triomflaan, take entrance 6. Coming from Terkamerenbos via Generaal Jacqueslaan, once you have passed train station Etterbeek, turn right on Pleinlaan, take entrance 11 or 13. Deze fiche werd gerealiseerd in juni 2014. De frequenties kunnen na verloop van tijd wijzigen. Last update: june 2014. The times and frequencies shown are subject to change

Accessible aux PMR avec aide, toegankelijk voor PBM met hulp Accessible for PRM with assistance

Fig 3.: Metro

Arrêt de surface, bovengrondse halte, aboveground stop

© 14-1789 - STIB-MIVB - 03/2014

Tram / Tramway