SEMINARS
Affine walled Brauer-Clifford superalgebras

2018-03-15　10:00 — 11:00

Middle Lecture Room

In this talk, a notion of affine walled Brauer-Clifford superalgebras $BC_{r, t}^{\rm aff}$ is introduced over an arbitrary integral domain $R$ containing $2^{-1}$. These superalgebras can be considered as affinization of walled Brauer superalgebras which are introduced by Jung and Kang. By constructing infinite many homomorphisms from $BC_{r, t}^{\rm aff}$ to a class of level two walled Brauer-Clifford superagebras over $\mathbb C$, we prove that $BC_{r, t}^{\rm aff}$ is free over $R$ with infinite rank.  Using a previous method on cyclotomic walled Brauer algebras, we prove that $BC_{k, r, t}$ is free over $R$ with super rank $(k^{r+t}2^{r+t-1} (r+t)!, k^{r+t}2^{r+t-1} (r+t)!)$ if and only if it is admissible. Finally, we give a proof of Comes-Kujawa's conjecture on the basis of cyclotomic oriented Brauer-Clifford supercategory and prove that the degenerate affine walled Brauer-Clifford superalgebras (resp., their cyclotomic quotients) defined by Comes and Kujawa are isomorphic to our degenerate affine walled Brauer-Clifford superalgebras (resp., their cyclotomic quotients).  This is a joint work with Mengmeng Gao, Hebing Rui and Yucai Su.