From Partition Identities to a Combinatorial Approach to Explicit Satake Inversion

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2018-09-01

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© 2018, Springer International Publishing AG, part of Springer Nature. In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands’ beyond endoscopy proposal. These partition identities motivate an explicit plethysm expansion of Sym jSym kV for GL 2 in the case k = 3. We compute the plethysm explicitly for the cases k = 3, 4. Moreover, we use these expansions to explicitly compute the basic function attached to the symmetric power L-function of GL 2 for these two cases.

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10.1007/s00026-018-0391-3

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Hahn, H, J Huh, E Lim and J Sohn (2018). From Partition Identities to a Combinatorial Approach to Explicit Satake Inversion. Annals of Combinatorics, 22(3). pp. 543–562. 10.1007/s00026-018-0391-3 Retrieved from https://hdl.handle.net/10161/22446.

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Hahn

Heekyoung Hahn

Associate Research Professor of Mathematics

Number Theory in the large: Automorphic represenations, Trace formula, Laplacian eigenfunctions and Littlewood-Richardson coefficients


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