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ABCD of qq-characters

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arxiv 2302.00525 v2 pith:U4OASM6I submitted 2023-02-01 hep-th math-phmath.MP

ABCD of qq-characters

classification hep-th math-phmath.MP
keywords qq-charactersgaugegroupsexpressionstheoriesabcdalgebraallows
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The qq-characters are powerful tools to reveal symmetries and integrabilities of Seiberg-Witten theories. The goal of this paper is to provide analytic expressions of qq-characters based on Young diagrams in 5d $\mathcal{N} = 1$ pure Yang-Mills theories with BCD-type gauge groups, by focusing on the unrefined limit. Using these expressions, we investigate the relationships among qq-characters of classical gauge groups. For SO(n) gauge groups, we construct a quantum-toroidal-like algebra via the Ward-identity approach, which allows us to derive the qq-characters.

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  1. Shell formulas for instantons and gauge origami

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    A new shell formula unifies and delivers explicit closed-form expressions plus recursions for instanton partition functions in 5d SYM and multiple gauge origami configurations using arbitrary-dimensional Young diagrams.