From Partition Identities to a Combinatorial Approach to Explicit Satake Inversion
Abstract
© 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.
Type
Journal articleSubject
Science & TechnologyPhysical Sciences
Mathematics, Applied
Mathematics
partition identities
multiplicities in the plethysm expansion
explicit Satake inversions
REPRESENTATIONS
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https://hdl.handle.net/10161/22446Published Version (Please cite this version)
10.1007/s00026-018-0391-3Publication Info
Hahn, H; Huh, J; Lim, E; & Sohn, J (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.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
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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