Shintarou Yanagida

Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial

Abstract We give an explicit formula of Whittaker vector for Virasoro algebra in terms of the Jack symmetric functions. Our fundamental tools are the Feigin–Fuchs bosonization and the split expression of the Calogero–Sutherland model given by Awata, Matsuo, Odake and Shiraishi.

FIVE-DIMENSIONAL SU(2) AGT CONJECTURE AND RECURSIVE FORMULA OF DEFORMED GAIOTTO STATE

This note deals with the five-dimensional pure SU(2) AGT conjecture proposed by Awata and Yamada. We give a conjecture on a recursive formula for the inner product of the deformed Gaiotto state. We also show that the K-theoretic pure SU(2) Nekrasov partition function satisfies the same recursion relation. Therefore the five-dimensional AGT conjecture is reduced to our conjectural recursive formula.

Norm of Logarithmic Primary of Virasoro Algebra

We give an algebraic proof of the formula on the norm of logarithmic primary of Virasoro algebra, which was proposed by Al. Zamolodchikov. This formula appears in the recursion formula for the norm of Gaiotto state, which guarantees the AGT relation for the four-dimensional SU(2) pure gauge theory.