Related papers: On parabolic Whittaker functions
We construct a power series representation of the integrals of form \begin{equation} \text{log} \int d\mu_{S}(\psi, \bar{\psi}) \hspace{0.05 cm} e^{f(\psi, \bar{\psi}, \eta, \bar{\eta})} \nonumber \end{equation} where $\psi, \bar{\psi}$ and…
We give an equivalent finitary reformulation of the classical Shannon-McMillan-Breiman theorem which has an immediate translation to the case of ergodic quantum lattice systems. This version of a quantum Breiman theorem can be derived from…
We study a class of representations of the Lie algebra of Laurent polynomials with values in the nilpotent subalgebra of sl(3). We derive Weyl-type (bosonic) character formulas for these representations. We establish a connection between…
Let G be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group ^LG in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian Gr_G=G((t))/G[[t]] of the…
Integrable delay analogues of the two-dimensional Toda lattice equation are presented and their muti-soliton solutions are constructed by applying the delay reduction to the Gram determinant solution.
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
We generalize the Toda lattice (or Toda chain) equation to the square lattice; i.e., we construct an integrable nonlinear equation, for a scalar field taking values on the square lattice and depending on a continuous (time) variable,…
We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…
We represent Feigin's construction [11] of lattice W algebras and give some simple results: lattice Virasoro and $W_3$ algebras. For simplest case $g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We find simplest…
Some aspects of Aomoto's generalized hypergeometric functions on Grassmannian spaces $Gr(k+1,n+1)$ are reviewed. Particularly, their integral representations in terms of twisted homology and cohomology are clarified with an example of the…
By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…
In 1978 Kostant suggested the Whittaker model of the center of the universal enveloping algebra U(g) of a complex simple Lie algebra g. The main result is that the center of U(g) is isomorphic to a commutative subalgebra in U(b), where b is…
Recently integral representations for the eigenfunctions of quadratic open Toda chain Hamiltonians for classical groups was proposed. This representation generalizes Givental representation for A_n. In this note we verify that the wave…
We quantize $sl_n$ Toda field theories in a periodic lattice. We find the quantum exchange algebra in the diagonal monodromy (Bloch wave) basis in the case of the defining representation. In the $sl_3$ case we extend the analysis also to…
We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation…
In this paper we present a general vacuum solution of the modified Gauss-Bonnet gravity equations for the Friedmann-Lema\^itre-Robertson-Walker metric. We use an ansatz to reduce the gravitational equations to an ordinary differential…
We establish integral analogues of results of Bushnell and Henniart for spaces of Whittaker functions arising from the groups GL_n(F) for F a p-adic field. We apply the resulting theory to the existence of representations arising from the…
We show that the k-double Schur functions defined by the authors, and the quantum double Schubert polynomials studied by Kirillov and Maeno and by Ciocan-Fontanine and Fulton, can be obtained from each other by an explicit rational…
In this paper the spherical case of the Whittaker Inversion Theorem is given a relatively self-contained proof. This special case can be used as a help in deciphering the handling of the continuous spectrum in the proof of the full theorem.…
Let $p$ and $l$ be distinct odd primes and let $n\geq 2$ be a positive integer. Let $E$ be a finite Galois extension of degree $l$ of a $p$-adic field $F$. Let $q$ be the cardinality of the residue field of $F$. Let $\overline{\pi}_F$ be a…