Generalized Steinberg relations

On Extensions of generalized Steinberg Representations

Let F be a local non-archimedean field and let G be the group of F valued points of a connected reductive algebraic group over F. In this paper we compute the Ext-groups of generalized Steinberg representations in the category of smooth G-representations with coefficients in a certain self-injective ring. AMS 2000 Mathematics subject classification: Primary 22E50. Secondary 11F70.

Tensoring Generalized Characters with the Steinberg Character

Let G be a reductive connected algebraic group over an algebraic closure of a finite field of characteristic p. Let F be a Frobenius endomorphism on G and write G := G F for the corresponding finite group of Lie type. We consider projective characters of G in characteristic p of the form St ·β, where β is an irreducible Brauer character and St the Steinberg character of G. Let M be a rational G...

Homology of Generalized Steinberg Varieties and Weyl Group Invariants

Let G be a complex, connected, reductive algebraic group. In this paper we show analogues of the computations by Borho and MacPherson of the invariants and antiinvariants of the cohomology of the Springer fibres of the cone of nilpotent elements, N , of Lie(G) for the Steinberg variety Z of triples. Using a general specialization argument we show that for a parabolic subgroup WP ×WQ of W × W th...

Generalized Uncertainty Relations:

Relations on generalized degree sequences

We study degree sequences for simplicial posets and polyhedral complexes, generalizing the well-studied graphical degree sequences. Here we extend the more common generalization of vertex-to-facet degree sequences by considering arbitrary face-to-flag degree sequences. In particular, these may be viewed as natural refinements of the flag f -vector of the poset. We investigate properties and rel...