On Lusztig's isomorphism theorem for Hecke algebras

On Iwahori–hecke Algebras with Unequal Parameters and Lusztig’s Isomorphism Theorem

By Tits’ deformation argument, a generic Iwahori–Hecke algebra H associated to a finite Coxeter group W is abstractly isomorphic to the group algebra of W . Lusztig has shown how one can construct an explicit isomorphism, provided that the Kazhdan–Lusztig basis of H satisfies certain deep properties. If W is crystallographic and H is a one-parameter algebra, then these properties are known to h...

The Satake Isomorphism for Special Maximal Parahoric Hecke Algebras

Let G denote a connected reductive group over a nonarchimedean local field F . Let K denote a special maximal parahoric subgroup of G(F ). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F ). The key ingredient is a Cartan decomposition describing the double coset space K\G(F )/K. We also describe how our results relate to the trea...

Another runner removal theorem for v-decomposition numbers of Iwahori–Hecke algebras and q-Schur algebras

Let F denote the Fock space representation of the quantum groupUv(ŝle). The ‘v-decomposition numbers’ are the coefficients when the canonical basis for this representation is expanded in terms of the basis of partitions, and the evaluations at v = 1 of these polynomials give the decomposition numbers for Iwahori–Hecke algebras and q-Schur algebras over C. James and Mathas have proved a theorem ...

Hecke Algebras

which is Artin’s braid relation. In general we will refer to (1) as the braid relation satisfied by si and sj. In order for W to be a Coxeter group it is required that the given set of relations between elements of I give a presentation of W . Informally, this means that any relation between generators in I can be deduced from the fact that the s ∈ Σ have order 2 and the braid relations. Formal...

On Isomorphism of Simplicial Complexes and Their Related Algebras