A Selberg integral for the Lie algebra A_n

Abstract

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.

32 pages

Cited by in corpus (12)

• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• Integrable structure, W-symmetry and AGT relation
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• The sl_3 Selberg integral
• Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral
• The ${\mathbb{F}}_p$-Selberg integral of type $A_n$
• AFLT-type Selberg integrals
• Some recursive formulas for Selberg-type integrals
• Singular vectors for the $W_N$ algebras
• The singularities of Selberg- and Dotsenko-Fateev-like integrals
• Proof of 5D $A_n$ AGT conjecture at $\beta =1$
• Algebras of Non-Local Screenings and Diagonal Nichols Algebras