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We formulate a Satake isomorphism for the integral spherical Hecke algebra of an unramified $p$-adic group $G$ and generalize the formulation to give a description of the Hecke algebra $H_G(V)$ of weight $V$, where $V$ is a lattice in an irreducible algebraic representation of $G$.
For certain characters of the compact torus of a reductive $p$-adic group, which we call strongly parabolic characters, we prove Satake-type isomorphisms. Our results generalize those of Satake, Howe, Bushnell and Kutzko, and Roche.
This article constructs the Satake parameter for any irreducible smooth $J$-spherical representation of a $p$-adic group, where $J$ is any parahoric subgroup. This parametrizes such representations when $J$ is a special maximal parahoric subgroup. Th
We give a short proof based on Lusztigs generalized Springer correspondence of some results of [BrCh,BaCr,P].
Let k be an algebraically closed field. It is known that any stable equivalence between standard representation-finite self-injective k-algebras (without blocks of Lowey length 2) lifts to a standard derived equivalence, in particular, it is of Morit
Let ($mathfrak{g},mathsf{g})$ be a pair of complex finite-dimensional simple Lie algebras whose Dynkin diagrams are related by (un)folding, with $mathsf{g}$ being of simply-laced type. We construct a collection of ring isomorphisms between the quantu