On universal Baxter operator for classical groups

2011/04/03 by Anton A. Gerasimov, Gerasimov, Anton A., Dimitri R. Lebedev +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT) #math-ph #math.MP #math.RT

paper · pdf · doi:10.48550/arxiv.1104.0420

12 pages

arxiv created 2011/04/03 · arxiv updated 2011/04/05

Abstract

The universal Baxter operator is an element of the Archimedean spherical Hecke algebra H(G,K), K be a maximal compact subgroup of a Lie group G. It has a defining property to act in spherical principle series representations of G via multiplication on the corresponding local Archimedean L-factors. Recently such operators were introduced for G=GL_ℓ+1(R) as generalizations of the Baxter operators arising in the theory of quantum Toda chains. In this note we provide universal Baxter operators for classical groups SO_2ℓ, Sp_2ℓ using the results of Piatetski-Shapiro and Rallis on integral representations of local Archimedean L-factors.

Related

• The Hecke-Baxter operators via Heisenberg group extensions
• The GL_ℓ+1(ℝ) Hecke-Baxter operator: principal series representations
• Global GL₂ Hecke-Baxter operator
• On Baxter Q-operators And Their Arithmetic Implications
• Rota-Baxter operators on compact simple Lie groups and algebras