Throughout this paper, G denotes a fixed, not necessarily connected, reductive algebraic group over an algebraically closed field k. This paper is a part of a series [L9] which attempts to develop a theory of character sheaves on G. The usual convolution of class functions on a connected reductive group over a finite field makes sense also for complexes in D(G0) and then it preserves (see [Gi])...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

We consider a family of singular infinite dimensional unitary representations of G = Sp(n,R) which are realized as sheaf cohomology spaces on an open G-orbit D in a generalized flag variety for the complexification of G. By parametrizing an appropriate space, MD, of maximal compact subvarieties in D, we identify a holomorphic double fibration between D and MD which we use to define a map P , of...

DMITRY KERNER AND VICTOR VINNIKOV Abstract. Let M be a d×d matrix whose entries are linear forms in the homogeneous coordinates of P2. Then M is called a determinantal representation of the curve {det(M) = 0}. Such representations are well studied for smooth curves. We study determinantal representations of curves with arbitrary singularities (mostly reduced). The kernel of M defines a torsion ...

We show that two Weyl group actions on the Springer sheaf with arbitrary coefficients, one defined by Fourier transform and one by restriction, agree up to a twist by the sign character. This generalizes a familiar result from the setting of l-adic cohomology, making it applicable to modular representation theory. We use the Weyl group actions to define a Springer correspondence in this general...

For a simply-connected simple algebraic group G over C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of G, generalizing a well-known fact about GLn. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number ...

In [Sco] D. Scott has shown how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion à la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly in [Fou, Hay].

We describe the cohomology of sheaf twisted differential operators on quantized flag manifold at a root unity whose order is prime power. It follows from this and our previous results that for De Concini-Kac type enveloping algebra, where parameter q specialized to power, number irreducible modules with certain specified central character coincides dimension total group corresponding Springer f...

We use the Springer correspondence to give a partial characterization of irreducible representations which appear in Tymoczko dot action Weyl group on cohomology ring regular semisimple Hessenberg variety. In type A, we apply these techniques prove that all summands pushforward constant sheaf universal family have full support. also observe recent results Brosnan and Chow, local invariant cycle...

Abstract The van Est map is a from Lie groupoid cohomology (with respect to sheaf taking values in representation) algebroid cohomology. We generalize the allow for more general sheaves, namely sheaves of sections (smooth or holomorphic) $G$-module, where $G$-modules are structures, which differentiate representations. Many geometric structures involving groupoids and stacks classified by not r...