Mathias Pétréolle
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A Nekrasov-Okounkov type formula for affine ˜C
dmtcs:2498 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2015,
DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
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https://doi.org/10.46298/dmtcs.2498
A Nekrasov-Okounkov type formula for affine ˜CConference paper
Authors: Mathias Pétréolle 1
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Mathias Pétréolle
1 Combinatoire, théorie des nombres
In 2008, Han rediscovered an expansion of powers of Dedekind η function due to Nekrasov and Okounkov by using Macdonald's identity in type ˜A. In this paper, we obtain new combinatorial expansions of powers of η, in terms of partition hook lengths, by using Macdonald's identity in type ˜C and a new bijection. As applications, we derive a symplectic hook formula and a relation between Macdonald's identities in types ˜C, ˜B, and ~BC.