Related papers: On the Determination of the Plancherel measure for…
We relate the analytic conductor of a generic irreducible representation of $\mathrm{GL}_n(\mathbb{R})$ to the invariance properties of vectors in that representation. The relationship is an analytic archimedean analogue of some aspects of…
We consider the generalization of Kleshchev's lowering operators obtained by raising all the Carter-Lusztig operators in their definition to a power less than the characteristic of the ground field. If we apply such an operator to a nonzero…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…
Inspired by work of Ladkani, we explain how to construct generalisations of the classical reflection functors of Bern\v{s}te\u{\i}n, Gel'fand and Ponomarev by means of the Grothendieck construction.
We compute explicitly traces of the Dirichlet form related to the Bessel process with respect to discrete measures as well as measures of mixed type. Then some global properties of the obtained Dirichlet forms, such as conservativeness,…
An extension of the Newell-Whitehead-Segel amplitude equation covariant under abritrary rotations is derived systematically by the renormalization group method.
Here using some methods of combinatorial set theory, particularly the ones related to the construction of independent families of sets and some modified version of the notion of small sets originally introduced by Riecan, Riecan and…
We give a formula for a birational map on the Schubert cell associated to each Weyl group element of $G=\text{GL}(n)$. The map simplifies the UDL decomposition of matrices, providing structural insight into the Schubert cell decomposition…
This paper establishes a combinatorial link between different approaches to constructing Whittaker functions on a metaplectic group over a non-archimedean local field. We prove a metaplectic analogue of Tokuyama's Theorem and give a crystal…
A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation…
We prove the Plancherel formula for a four-parameter family of discrete Fourier transforms and their multivariate generalizations stemming from corresponding generalized Schur polynomials. For special choices of the parameters, this…
We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's…
We prove variation-norm estimates for the Walsh model of the truncated bilinear Hilbert transform, extending related results of Lacey, Thiele, and Demeter. The proof uses analysis on the Walsh phase plane and two new ingredients: (i) a…
We exploit the idea that the character of an irreducible finite dimensional $\mathfrak{gl}_n$-module is the sum of certain exponents of integer points in a Gelfand-Tsetlin polytope and can thus be calculated via Brion's theorem. In order to…
The mass of the glueballs is calculated in the B.S. equation framework. Under instantaneous approximation, the wave function of B.S. equations are obtained. The kernel is chosen as the sum of an one-gluon exchange potential, a contact…
Several new properties of weighted Hilbert transform are obtained. If mu is zero, two Plancherel-like equations and the isotropic properties are derived. For mu is real number, a coerciveness is derived and two iterative sequences are…
In this paper we study the restrictions of the minimal representation in the analytic continuation of the scalar holomorphic discrete series from $Sp(n,\mathbb{R})$ to $GL(n,\mathbb{R})$, and from SU(n,n) to $GL(n,\mathbb{C})$ respectively.…
We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.
Let F be a non-archimedean local field of characteristic zero. Jacquet, Piatetski-Shapiro and Shalika introduced the notion of newforms for irreducible generic representations of GL_n(F). In this paper, we give an explicit formula for…