Gustafson integrals for $SL(2,\mathbb{C})$ spin magnet

Abstract

It was observed recently that the multidimensional Mellin--Barnes integrals (Gustafson's integrals) arise naturally in studies of the $SL(2,R)$ spin chain models. We extend this analysis to the noncompact $SL(2,\mathbb{C})$ spin magnets and obtain integrals which generalize Gustafson's integrals to the complex case.

11 pages, 2 figures

References in corpus (3)

• Exact solution of the Faddeev-Volkov model
• Quantum mechanics of null polygonal Wilson loops
• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet

Cited by in corpus (4)

• Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group
• On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions
• BC-type open $SL(2,\mathbb{C})$ spin chain
• The Gelfand-Tsetlin basis for infinite-dimensional representations of $g{l}_n(\mathbb{C})$