Diagram automorphisms and canonical bases for quantum groups

MS Seminar (Mathematics – String Theory)

Speaker:Toshiaki Shoji (Tongji University)
Title:Diagram automorphisms and canonical bases for quantum groups
Date (JST):Tue, Sep 21, 2021, 13:30 – 15:00
Place:Online
Abstract:Let U be the quantum group associated to a Kac-Moody algebra of symmetric type,

and U_1 the quantum group obtained from an admissible diagram automorphism s on U.

Let U^-, U_1^- be the negative part of U, U_1, respectivey. Lusztig constructed

the canonical basis B of U^- , and the canonical signed basis (B_1)’ of U_1^-,

by using the geometric theory of quivers. Then he constructed the canonical basis B_1 of U_1^-

from (B_1)’ by using Kashiwara’s theory of crystals, and obtained the natural bijection
between the set B^s of s-fixed elements in B and B_1.

In this talk, we take a different approach for this problem. Assuming
the existence of the canonical basis B of U^-, we construct the canonical
signed basis (B_1)’ of U_1^- , and the bijection between (B’)^s and (B_1)’,
in an elmentary way. In the case where the order of s is odd, we can construct

the canonical basis B_1, and the bijection between B^s and B_1.
Organizers:G. Dmitrii, T. Milanov, M. Yamazaki
Contact:seminar-organizer _at_ ipmu.jp

Date

Sep 21 2021
Expired!

Time

Japan Standard Time
1:30 pm - 3:00 pm

Local Time

  • Timezone: America/New_York
  • Date: Sep 21 2021
  • Time: 12:30 am - 2:00 am

More Info

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Domain

Theoretical Physics

Location

Virtual

Location 2

(IPMU) The Kavli Institute for Physics and Mathematics of the Universe at the University of Tokyo

Organizer

(IPMU) The Kavli Institute for Physics and Mathematics of the Universe at the University of Tokyo
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