Cauchy formula and the character ring

Abstract

Cauchy summation formula plays a central role in application of character calculus to many problems, from AGT-implied Nekrasov decomposition of conformal blocks to topological-vertex decompositions of link invariants. We briefly review the equivalence between Cauchy formula and expressibility of skew characters through the Littlewood-Richardson coefficients. As not-quite-a-trivial illustration we consider how this equivalence works in the case of plane partitions -- at the simplest truly interesting level of just four boxes.

9 pages

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Cited by in corpus (15)

• A slow review of the AGT correspondence
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Hunt for 3-Schur polynomials
• Quantization of Harer-Zagier formulas
• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• Tensorial generalization of characters
• 3-Schurs from explicit representation of Yangian $Y({\widehat{\mathfrak{gl}}}_1)$. Levels 1-5
• On Hamiltonians for Kerov functions
• Pentad and triangular structures behind the Racah matrices
• Macdonald polynomials for super-partitions
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• On character expansion and Gaussian regularization of Itzykson-Zuber measure
• Superintegrability and Kontsevich-Hermitian relation
• Equating Schur Functions
• Itzykson-Zuber correlators from character expansion