On a conjecture of Braverman and Kazhdan
نویسندگان
چکیده
In this paper a proof of Conjecture 9.12 of Braverman–Kazhdan in their article γ-functions of representations and lifting on the acyclicity of their l-adic γ-sheaves over certain affine spaces is given for GL(n).
منابع مشابه
Gindikin-Karpelevich finiteness for Kac-Moody groups over local fields
In this paper, we prove some finiteness results about split Kac-Moody groups over local non-archimedean fields. Our results generalize those of "An affine GindikinKarpelevich formula" by Alexander Braverman, Howard Garland, David Kazhdan and Manish Patnaik. We do not require our groups to be affine. We use the hovel I associated to this situation, which is the analogue of the Bruhat-Tits buildi...
متن کاملBrundan-kazhdan-lusztig and Super Duality Conjectures
We formulate a general super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebras of type A, based on a Fock space formalism of their Kazhdan-Lusztig theories which was initiated by Brundan. We show that the Brundan-Kazhdan-Lusztig (BKL) polynomials for gl(m|n) in our parabolic setup can be identified with the usual parabolic Kazhda...
متن کاملOn the formal arc space of a reductive monoid
The formal arc space L X of an algebraic variety X carries an important amount of information on singularities of X . Little is known about singularities of the formal arc scheme itself. According to Grinberg, Kazhdan [12] and Drinfeld [9] it is known, nevertheless, that the singularity of L X at a non-degenerate arc is finite dimensional i.e. for every non-degenerate arc x ∈L X , the formal co...
متن کاملHandsaw Quiver Varieties and Finite W -algebras
Following Braverman–Finkelberg–Feigin–Rybnikov (arXiv: 1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W -algebra of type A. This is a finite analog of the AGT conjecture on 4-dimensional supersymmetric Yang–Mills theory with surface operators. Our new observation is that the C-fixed point set of a handsaw quiver variety is...
متن کاملThe Kazhdan-Lusztig polynomial of a matroid
We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M , in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincaré polynomials. We al...
متن کامل