Givental Integral Representation for Classical Groups
نویسنده
چکیده
We propose integral representations for wave functions of Bn, Cn, and Dn open Toda chains at zero eigenvalues of the Hamiltonian operators thus generalizing Givental representation for An. We also construct Baxter Q-operators for closed Toda chains corresponding to Lie algebras B∞, C∞, D∞, affine Lie algebras B (1) n , C (1) n , D (1) n and twisted affine Lie algebras A (2) 2n−1 and A (2) 2n . Our approach is based on a generalization of the connection between Baxter Q-operator for A (1) n closed Toda chain and Givental representation for the wave function of An open Toda chain uncovered previously. To be published in the Proceedings of the Satellite ICM 2006 conference: ”Integrable systems in Applied Mathematics”, Colmenarejo (Madrid, Spain), 7-12 September 2006. E-mail: [email protected] E-mail: [email protected]
منابع مشابه
Baxter Q-operator and Givental Integral Representation for C N and D N
Recently integral representations for the eigenfunctions of quadratic open Toda chain Hamiltonians for classical groups was proposed. This representation generalizes Givental representation for An. In this note we verify that the wave functions defined by these integral representations are common eigenfunctions for the complete set of open Toda chain Hamiltonians. We consider the zero eigenvalu...
متن کاملA representation for some groups, a geometric approach
In the present paper, we are going to use geometric and topological concepts, entities and properties of the integral curves of linear vector fields, and the theory of differential equations, to establish a representation for some groups on $R^{n} (ngeq 1)$. Among other things, we investigate the surjectivity and faithfulness of the representation. At the end, we give some app...
متن کاملSome bounds on unitary duals of classical groups - non-archimeden case
We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups. Roughly, they can show up only if the central character of the inducing irreducible cuspidal representation is dominated by the square root of the modular character of the minimal parabolic subgroup. For unitarizable subquotients...
متن کاملBaxter operator and Archimedean Hecke algebra
In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gll+1 and so2l+1. Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in terms of Gammafunctions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral...
متن کاملFinite groups admitting a connected cubic integral bi-Cayley graph
A graph is called integral if all eigenvalues of its adjacency matrix are integers. Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$. In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.
متن کامل