Affine Flag Varieties and Quantum Symmetric Pairs - Brossura

Fan, Zhaobing; Lai, Chun-ju; Li, Yiqiang; Luo, Li; Wang, Weiqiang

Brossura

ISBN 10: 1470441756 ISBN 13: 9781470441753

Casa editrice: Amer Mathematical Society, 2020

Riassunto

The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$. In this paper the authors study the structures of Schur algebras and Lusztig algebras associated to (four variants of) partial flag varieties of affine type $C$.

The authors show that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine $\mathfrak{sl}$ and $\mathfrak{gl}$ types, respectively. In this way, the authors provide geometric realizations of eight quantum symmetric pairs of affine types. They construct monomial and canonical bases of all these quantum (Schur, Lusztig, and coideal) algebras.

For the idempotented coideal algebras of affine $\mathfrak{sl}$ type, the authors establish the positivity properties of the canonical basis with respect to multiplication, comultiplication and a bilinear pairing. In particular, the authors obtain a new and geometric construction of the idempotented quantum affine $\mathfrak{gl}$ and its canonical basis.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2020
• Lingua: Inglese
• ISBN 10: 1470441756
• ISBN 13: 9781470441753
• Rilegatura: Copertina flessibile
• Numero di pagine: 123
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile