From Partition Identities to a Combinatorial Approach to Explicit Satake Inversion

Heekyoung Hahn; Ji Sun Huh; Eun Sung Lim; Jaebum Sohn

doi:10.1007/s00026-018-0391-3

From Partition Identities to a Combinatorial Approach to Explicit Satake Inversion

Heekyoung Hahn, Ji Sun Huh, Eun Sung Lim, Jaebum Sohn

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	543-562
Number of pages	20
Journal	Annals of Combinatorics
Volume	22
Issue number	3
DOIs	https://doi.org/10.1007/s00026-018-0391-3
Publication status	Published - 2018 Sept 1

Bibliographical note

Funding Information:
∗The fourth named author is thankful for generous support by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2017R1A2B4009501).

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1007/s00026-018-0391-3

Cite this

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abstract = "In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands{\textquoteright} 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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N1 - Funding Information: ∗The fourth named author is thankful for generous support by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2017R1A2B4009501). Publisher Copyright: © 2018, Springer International Publishing AG, part of Springer Nature.

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From Partition Identities to a Combinatorial Approach to Explicit Satake Inversion

Abstract

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