Related papers: Jacquet functor and De Concini-Procesi compactific…
We study torsion in the homology of arithmetic groups and give evidence that it plays a role in the Langlands program. We prove, among other results, a numerical form of a Jacquet--Langlands correspondence in the torsion setting.
We construct the generalized $\beta$ and $(q,t)$-deformed partition functions through $W$ representations, where the expansions are respectively with respect to the generalized Jack and Macdonald polynomials labeled by $N$-tuple of Young…
We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected)…
These lecture notes are based on lectures given by the author at the summer school "Arrangements in Pyr\'en\'ees" in June 2012. We survey and compare various compactifications of complex hyperplane arrangement complements. In particular, we…
On the basis of the generalizations of the Jacobi identity found by the author some identities satisfied by the curvature and torsion of a covariant differentiation are derived. A kind of the generalized covariant differentiation is…
It is shown that quadratic constraints are compatible with the geometric integrability scheme of the multidimensional quadrilateral lattice equation. The corresponding Ribaucour reduction of the fundamental transformation of quadrilateral…
We consider the Cohen-Macaulay compactification of the space of twisted cubics in projective n-space. This compactification is the fine moduli scheme representing the functor of CM-curves with Hilbert polynomial 3t+1. We show that the…
We proof the homogenization of the Hamilton-Jacobi equation on arbitrary compact manifolds using Evans perturbed test function method.
For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphic symplectic form making the fibration…
In this paper, we give geometric realizations of Lusztig's symmetries. We also give projective resolutions of a kind of standard modules. By using the geometric realizations and the projective resolutions, we obtain the categorification of…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.
In this article we give a result obtained of an experimental way for the Euler totient function.
This work is devoted to the algebraic and arithmetic properties of Rankin-Cohen brackets allowing to define and study them in several natural situations of number theory. It focuses on the property of these brackets to be formal…
We construct the reflection functors for quiver Hecke algebras of an arbitrary symmetrizable Kac-Moody type. These reflection functors categorify Lusztig's braid symmetries.
A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and…
Using a super-realization of the Wigner-Heisenberg algebra a new realization of the q-deformed Wigner oscillator is implemented.
We realize some powers of Dedekind $\eta$-function as traces on quantum coordinate algebras.
In this paper we develop a fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives. The fractional action function is obtained and the solutions of the equations of motion are recovered. An…
We prove stochastic homogenization for a general class of coercive, nonconvex Hamilton-Jacobi equations in one space dimension. Some properties of the effective Hamiltonian arising in the nonconvex case are also discussed.