# Hecke–Clifford Superalgebras and Crystals of Type <em>D</em><sub><em>l</em></sub><sup>(2)</sup>

### Shunsuke Tsuchioka

Kyoto University, Japan

## Abstract

In [BK], Brundan and Kleshchev showed that some parts of the representation theory of the affine Hecke–Clifford superalgebras and its ﬁnite-dimensional “cyclotomic” quotients are controlled by the Lie theory of type *A_2_l*(2) when the quantum parameter *q* is a primitive (2_l_ + 1)-th root of unity. We show that similar theorems hold when *q* is a primitive 4_l_-th root of unity by replacing the Lie theory of type *A_2_l*(2) with that of *D__l*(2).

## Cite this article

Shunsuke Tsuchioka, Hecke–Clifford Superalgebras and Crystals of Type <em>D</em><sub><em>l</em></sub><sup>(2)</sup>. Publ. Res. Inst. Math. Sci. 46 (2010), no. 2, pp. 423–471

DOI 10.2977/PRIMS/13