Séminaire Lotharingien de Combinatoire, B54n (2007), 17 pp.

Alain Lascoux

Adding +-1 to the Argument of a Hall-Littlewood Polynomial

Abstract. Shifting by +-1 powers sums: pi -> pi +- 1 induces a transformation on symmetric functions that we detail in the case of Hall-Littlewood polynomials. By iteration, this gives a description of these polynomials in terms of plane partitions, as well as some generating functions. We recover in particular an identity of Warnaar related to Rogers-Ramanujan identities.

Received: September 5, 2007. Accepted: September 15, 2007. Final Version: September 16, 2007.

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