Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
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In this paper, an explicit formula of Whittaker vector for Virasoro algebra in terms of the Jack symmetric functions is given, using the split expression of the Calogero-Sutherland model given by Awata, Matsuo, Odake and Shiraishi.About:
This article is published in Journal of Algebra.The article was published on 2011-05-01 and is currently open access. It has received 70 citations till now. The article focuses on the topics: Whittaker function & Virasoro algebra.read more
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Instanton counting with a surface operator and the chain-saw quiver
Hiroaki Kanno,Yuji Tachikawa +1 more
TL;DR: In this paper, the authors describe the moduli space of SU(N) instantons in terms of the representations of the so-called chain-saw quiver, which allows them to write down the instanton partition function as a summation over the fixed point contributions labeled by Young diagrams.
Journal ArticleDOI
Proving AGT conjecture as HS duality: Extension to five dimensions
TL;DR: In this paper, the AGT relation was interpreted as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. But the problem with extra poles in individual Nekrasov functions still exists, therefore, such a proof works only for β = 1, i.e. for q=t in MacDonaldʼs notation.
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On AGT relations with surface operator insertion and a stationary limit of beta-ensembles
TL;DR: In this article, a summary of the AGT relations for conformal blocks with the addition insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, is presented.
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Conformal blocks and generalized Selberg integrals
TL;DR: In the free field model, these coefficients arise only with a special "conservation" relation imposed on the three dimensions of the operators involved in OPE as mentioned in this paper, where additional Dotsenko-Fateev integrals are inserted between the positions of the two original operators in the product.
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A direct proof of AGT conjecture at β = 1
TL;DR: The AGT conjecture implies the equality between Dotsenko-Fateev β-ensembles and the Nekrasov functions for SU(2) with β = 1, which corresponds to c = 1 at the conformal side and to ϵ1 + ϵ2 = 0 at the gauge theory side as discussed by the authors.
References
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Book
Symmetric functions and Hall polynomials
TL;DR: In this paper, the characters of GLn over a finite field and the Hecke ring of GLs over finite fields have been investigated and shown to be symmetric functions with two parameters.
Journal ArticleDOI
Seiberg-Witten Prepotential from Instanton Counting
TL;DR: In this article, a two-parameter generalization of the Seiberg-Witten prepotential is presented, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.
Journal ArticleDOI
Liouville Correlation Functions from Four-dimensional Gauge Theories
TL;DR: In this paper, the authors conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of SCFTs recently defined by one of the authors.
Book ChapterDOI
Seiberg-Witten theory and random partitions
Nikita Nekrasov,Andrei Okounkov +1 more
TL;DR: In this paper, the authors investigated various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.
Seiberg-Witten prepotential from instanton counting
TL;DR: In this paper, a two-parameter generalization of the Seiberg-Witten prepotential is presented, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy.