Elliptic $$\mathrm A_n$$ Selberg Integrals

Abstract We use the elliptic interpolation kernel due to the second author to prove an $$\mathrm A_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> extension of the elliptic Selberg integral. More generally, we obtain elliptic analogues of the $$\mathrm A_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> Kadell, Hua–Kadell and Alba–Fateev–Litvinov–Tarnopolsky (or AFLT) integrals.