 Award ID(s):
 2101392
 NSFPAR ID:
 10467751
 Publisher / Repository:
 The Combinatorics Consortium
 Date Published:
 Journal Name:
 Algebraic combinatorics
 ISSN:
 25895486
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract We generalize the shuffle theorem and its $(km,kn)$ version, as conjectured by Haglund et al. and Bergeron et al. and proven by Carlsson and Mellit, and Mellit, respectively. In our version the $(km,kn)$ Dyck paths on the combinatorial side are replaced by lattice paths lying under a line segment whose x and y intercepts need not be integers, and the algebraic side is given either by a Schiffmann algebra operator formula or an equivalent explicit raising operator formula. We derive our combinatorial identity as the polynomial truncation of an identity of infinite series of $\operatorname {\mathrm {GL}}_{l}$ characters, expressed in terms of infinite series versions of LLT polynomials. The series identity in question follows from a Cauchy identity for nonsymmetric Hall–Littlewood polynomials.more » « less

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Abstract We study the family of irreducible modules for quantum affine
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