Skew quantum Murnaghan-Nakayama rule
Matjaž Konvalinka
DOI: 10.1007/s10801-011-0312-6
Abstract
We extend recent results of Assaf and McNamara on a skew Pieri rule and a skew Murnaghan-Nakayama rule to a more general identity, which gives an elegant expansion of the product of a skew Schur function with a quantum power sum function in terms of skew Schur functions. We give two proofs, one completely bijective in the spirit of Assaf-McNamara's original proof, and one via Lam-Lauve-Sotille's skew Littlewood-Richardson rule. We end with some conjectures for skew rules for Hall-Littlewood polynomials.
Pages: 519–545
Keywords: keywords Pieri rule; murnaghan-Nakayama rule; Schur functions; Hall-Littlewood polynomials
Full Text: PDF
References
1. Assaf, S., McNamara, P.: A Pieri rule for skew shapes. J. Comb. Theory, Ser. A 118(1), 277-290 (2011) (with an appendage by T. Lam)
2. Assaf, S., McNamara, P.: A Pieri rule for skew shapes, slides from a talk at FPSAC (2010). Available at
3. Konvalinka, M.: Combinatorics of determinental identities. Ph.D. thesis. MIT, Cambridge, Massachusetts (2008), 129 pp.
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5. Macdonald, I.G.: Symmetric Functions and Hall Polynomials. Oxford University Press, Oxford (1999)
6. Ram, A.: Frobenius formula for the characters of the Hecke algebras. Invent. Math. 106(3), 461-488
2. Assaf, S., McNamara, P.: A Pieri rule for skew shapes, slides from a talk at FPSAC (2010). Available at
3. Konvalinka, M.: Combinatorics of determinental identities. Ph.D. thesis. MIT, Cambridge, Massachusetts (2008), 129 pp.
4. Lam, T., Lauve, A., Sottile, F.: Skew Littlewood-Richardson rules from Hopf algebras. Int. Math. Res. Not. 2011, 1205-1219 (2011).
5. Macdonald, I.G.: Symmetric Functions and Hall Polynomials. Oxford University Press, Oxford (1999)
6. Ram, A.: Frobenius formula for the characters of the Hecke algebras. Invent. Math. 106(3), 461-488
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