Related papers: Intertwining operators for representations of cove…

We continue our study of the poles of local Langlands L-functions through the theory of induced from supercuspidal representations of quasi-split groups. Here we study the odd special orthogonal groups, and hence determine poles of Rankin…

In general, in gauge field theories, physical observables are represented by gauge-invariant composite operators, such as the electromagnetic current. As we recently demonstrated in the context of the $U\left(1\right)$ and…

Let $G$ be a real reductive linear group in the Harish-Chandra class. Suppose that $P$ is a parabolic subgroup of $G$ with Langlands decomposition $P=MAN$. Let $\pi$ be an irreducible representation of the Levi factor $L=MA$. We give…

Recently, Venkatesh extended the category equivalence between affine algebraic groups and Harish-Chandra pairs, which was proved by the author in the supersymmetric context, to the situation of the Verlinde category in positive…

An interpretation of Hirota bilinear relations for classical $\tau$ functions is given in terms of intertwining operators. Noncommutative example of $U_q(sl_2)$ is presented.

In this paper we generalize the fermionic approach to the KP hierarchy sudgested in the papers of Kyoto school 1981-1984 (Sato,Jimbo, Miwa...). The main idea is that the components of the intertwiningoperators are in some sense a…

We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups $G$ to rank one subgroups $G_1$. For this we use the realizations of complementary…

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…

We show that intertwining operators for the discrete Fourier transform form a cubic algebra $\mathcal{C}_q$ with $q$ a root of unity. This algebra is intimately related to the two other well-known realizations of the cubic algebra: the…

Let $G$ be a connected reductive algebraic group over a non-Archimedean local field $K$, and let $g$ be its Lie algebra. By a theorem of Harish-Chandra, if $K$ has characteristic zero, the Fourier transforms of orbital integrals are…

This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…

We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…

We construct type $g\ell(n)$ Yangian algebra evaluations of order $N$ embedded in Heisenberg algebras and consider their representations having a highest weight. These Yangian algebra presentations depend on $nN$ parameters. We construct…

It has recently been observed that IIB string theory in the pp-wave background can be used to calculate certain quantities, such as the dimensions of BMN operators, as exact functions of the effective coupling lambda' = lambda/J^2. These…

Let G be a nonlinear double cover of the real points of a connected reductive complex algebraic group with simply laced root system. We establish a uniform character multiplicity duality theory for the category of Harish-Chandra modules for…

We study intertwining relations for matrix one-dimensional, in general, non-Hermitian Hamiltonians by matrix differential operators of arbitrary order. It is established that for any matrix intertwining operator Q_N^- of minimal order N…

We present a new proof of Harish-Chandra's formula $$\Pi(h_1) \Pi(h_2) \int_G e^{\langle \mathrm{Ad}_g h_1, h_2 \rangle} dg = \frac{ [ \! [ \Pi, \Pi ] \!] }{|W|} \sum_{w \in W} \epsilon(w) e^{\langle w(h_1),h_2 \rangle},$$ where $G$ is a…

The main object of this work is to show how some rather elementary techniques based upon certain inverse pairs of symbolic operators would lead us easily to several decomposition formulas associated with confluent hypergeometric functions…

Let $G/K$ be a Hermitian symmetric space and $V_\tau$ an irreducible representation of $K$. We study the ring $\mathcal D^G(G/K, V_\tau)$ of $G$-invariant differential operators on sections of vector bundles $G\times_{(K, \tau)} V_\tau$…

In this note, we express explicitly the Dunkl kernel and generalized Bessel functions of type $A_{n-1}$ by the Humbert's function $\Phi_{2}^{(n)}$, with one variable specified. The obtained formulas lead to a new proof of Xu's integral…