Quantum cohomology of Hilbn(C2) and the weighted hook walk on Young diagrams

JOURNAL OF ALGEBRA

卷:349

Article

Ciocan-Fontanine, Ionut^2,3  Konvalinka, Matjaz¹  Pak, Igor⁴ 

[1] Univ Ljubljana, Dept Math, Ljubljana 1000, Slovenia

[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

[3] Korea Inst Adv Study, Sch Math, Seoul 130722, South Korea

[4] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

关键词: Hilbert scheme of points;    Quantum cohomology;    Hook walk;    Hook-length formula;   

DOI  :  10.1016/j.jalgebra.2011.10.011

来源: Elsevier

【 摘 要 】

Following the work of Okounkov and Pandharipande (2010) [OP1, OP2], Diaconescu [D], and the recent work of I. Ciocan-Fontanine et al. (in preparation) [CDKM] studying the equivariant quantum cohomology Q H*((C*)2)(Hilb(n)) of the Hilbert scheme and the relative Donaldson-Thomas theory of P-1 X C-2, we establish a connection between the J-function of the Hilbert scheme and a certain combinatorial identity in two variables. This identity is then generalized to a multivariate identity, which simultaneously generalizes the branching rule for the dimension of irreducible representations of the symmetric group in the staircase shape. We then establish this identity by a weighted generalization of the Greene-Nijenhuis-Wilf hook walk, which is of independent interest. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free