A Nekrasov-Okounkov type formula for affine \(\widetilde{C}\). (English. French summary) Zbl 1335.05014
Proceedings of the 27th international conference on formal power series and algebraic combinatorics, FPSAC 2015, Daejeon, South Korea, July 6–10, 2015. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 535-546 (2015).
Summary: G.-N. Han [Ann. Inst. Fourier 60, No. 1, 1–29 (2010; Zbl 1215.05013)] rediscovered an expansion of powers of Dedekind \(\eta\) function due to N. A. Nekrasov and A. Okounkov [Progress in Mathematics 244, 525–596 (2006; Zbl 1233.14029)] by using Macdonald’s identity in type \(\widetilde{A}\). In this paper, we obtain new combinatorial expansions of powers of \(\eta\), in terms of partition hook lengths, by using Macdonald’s identity in type \(\widetilde{C}\) and a new bijection. As applications, we derive a symplectic hook formula and a relation between Macdonald’s identities in types \(\widetilde{C}\), \(\widetilde{B}\), and \(\widetilde{BC}\).
For the entire collection see [Zbl 1333.05004].
For the entire collection see [Zbl 1333.05004].
MSC:
| 05A15 | Exact enumeration problems, generating functions |
| 05A17 | Combinatorial aspects of partitions of integers |
| 05A19 | Combinatorial identities, bijective combinatorics |
| 11B75 | Other combinatorial number theory |
| 11P82 | Analytic theory of partitions |
| 17B22 | Root systems |
