Z2-graded Clifford system in the Hecke algebra of type Bn

Alternating Subalgebras of Hecke Algebras and Alternating Subgroups of Braid Groups

“…Due to the relations (8)- (9), this map extends to a (surjective) homomorphism, which we denote again by , from the algebra to H + G . We shall prove that is an isomorphism.…”

“…The verification is straightforward (use (8)- (9)). On the other hand, one directly verifies that the map…”

Involutions of Iwahori–Hecke Algebras and Representations of Fixed Subalgebras

“…One can readily check that these direct sum decompositions satisfy the condition of the Z 2 -crossed product. 6 The branching rules for the Hecke algebras of Type B Let K 0 = Q(u, q) be the quotient field of R 0 and K 1 = Q(q) that of R 1 . Let λ = (λ (1) , λ (2) ) be a 2-tuple of Young diagrams of total size n. Let T = (T (1) , T (2) ) be a tableau of shape λ.…”

“…Since the Iwahori-Hecke algebra of type A can be considered as a q-analogue of the symmetric group, we defined the q-analogue of the alternating group as a subalgebra of it. An extension of [5] to the Hecke algebra of type B was given in [6]. We showed that those subalgebras can be defined as fixed subalgebras by Goldman involutions of Hecke algebras in [6].…”

“…Goldman involution itself can be defined for generic (non-specialized) Iwahori-Hecke algebras of type B. We have already given the fixed subalgebra by Goldman involution in generic Iwahori-Hecke algebras of type B, and have determined the branching rule and a basic set of irreducible representations in [6] as follows. Theorem 6.2.…”