Degenerate affine Hecke–Clifford algebras and type Q Lie superalgebras

Abstract

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA),

Completely splittable representations of affine Hecke-Clifford algebras

“…We further show that these representations are parameterized by skew shifted Young diagrams with precise constraints depending on p and give a dimension formula in terms of the associated standard Young tableaux. We remark that in the special case when p = 0, our result confirms a conjecture of Wang and it has been independently obtained by Hill, Kujawa, and Sussan [5].…”

Frobenius character formula and spin generic degrees for Hecke-Clifford algebra

“…The precise form of the field K is not relevant in this paper and we could simply take K to be the algebraic closure of C(v 1/2 ) as well. The construction of the irreducible H c n,K -modules U λ in [5] can be streamlined by a straightforward v-analogue of the seminormal form construction of the irreducible H c n -modules given in [4] and independently in [16] (cf. [19,Section 7]).…”

Dirac Cohomology for Degenerate Affine Hecke-Clifford Algebras

“…It is straightforward to check that the above actions define an H Cl W (An−1) -module by verifying the defining relations of H Cl W (An−1) . Some details can be found in [HKS,Prop. 4.1.1].…”

“…Let us recall a construction of some H Cl n -modules in [HKS,Sect. 4], which is indeed modified from the module of type A n−1 in Section 5.1.…”

“…In type A n−1 , we follow the construction in [HKS,Sect. 4.1], which uses a Jucys-Murphy-type element.…”