Elliptic extension of Gustafson's $q$-integral of type $G_2$

Abstract

The evaluation formula for an elliptic beta integral of type $G_2$ is proved. The integral is expressed by a product of Ruijsenaars' elliptic gamma functions, and the formula includes that of Gustafson's $q$-beta integral of type $G_2$ as a special limiting case as $p\to 0$. The elliptic beta integral of type $B{C}_1$ by van Diejen and Spiridonov is effectively used in the proof of the evaluation formula.

33 pages, 5 figures. V2: The proofs of Lemmas 6.3 and 6.5 were simplified. V3: Typo corrected

References in corpus (3)

• Superconformal indices for N=1 theories with multiple duals
• Derivation of a $B{C}_n$ elliptic summation formula via the fundamental invariants
• A generalization of the Sears--Slater transformation and elliptic Lagrange interpolation of type $B{C}_n$