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 (1)

• On $W$-representations of $\beta$- and $q,t$-deformed matrix models