Séminaire Lotharingien de Combinatoire, 82B.14 (2019), 12 pp.

Cédric Lecouvey and Cristian Lenart

Combinatorics of generalized exponents

Abstract. We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type C_n, we obtain a combinatorial description of the generalized exponents based on symplectic King tableaux. We also present three applications of our combinatorial formula. Our methods are expected to extend to the orthogonal types.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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