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LLT polynomials in the Schiffmann algebra

  • Jonah Blasiak EMAIL logo , Mark Haiman , Jennifer Morse , Anna Pun and George H. Seelinger
Published/Copyright: April 23, 2024

Abstract

We identify certain combinatorially defined rational functions which, under the shuffle to Schiffmann algebra isomorphism, map to LLT polynomials in any of the distinguished copies Λ ( X m , n ) E of the algebra of symmetric functions embedded in the elliptic Hall algebra ℰ of Burban and Schiffmann. As a corollary, we deduce an explicit raising operator formula for the ∇ operator applied to any LLT polynomial. In particular, we obtain a formula for m s λ which serves as a starting point for our proof of the Loehr–Warrington conjecture in a companion paper to this one.

Award Identifier / Grant number: DMS-1855784

Award Identifier / Grant number: DMS-1855804

Funding statement: Authors were supported by NSF Grants DMS-1855784 (J. Blasiak) and DMS-1855804 (J. Morse).

Acknowledgements

We thank the referee for many helpful suggestions.

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Received: 2022-10-04
Revised: 2024-02-10
Published Online: 2024-04-23
Published in Print: 2024-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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