Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA

Abstract

We construct Gaiotto states with fundamental multiplets in $SU(N)$ gauge theories, in terms of the orthonormal basis of spherical degenerate double affine Hecke algebra (SH in short), the representations of which are equivalent to those of $W_n$ algebra with additional $U(1)$ current. The generalized Whittaker conditions are demonstrated under the action of SH, and further rewritten in terms of $W_n$ algebra. Our approach not only consists with the existing literature but also holds for general $SU(N)$ case.

arXiv comment20 pages, 2 figures; v2: minor modifications, typos corrected

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• Virasoro irregular conformal block and beta deformed random matrix model
• Yangian associated with 2D $\mathcal{N}=1$ SCFT
• Argyres-Douglas theories and Liouville Irregular States
• On the Jeffrey-Kirwan residue of BCD-instantons
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Matching branches of non-perturbative conformal block at its singularity divisor
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Irregular conformal block, spectral curve and flow equations
• q-Vertex Operator from 5D Nekrasov Function
• Recursive Method for Nekrasov partition function for classical Lie groups
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• ABCD of qq-characters
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• Irregular matrix model with $\mathcal{W}$ symmetry
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Charge functions for odd dimensional partitions