Journal article
A Proof of the Extended Delta Conjecture
FORUM OF MATHEMATICS PI, v 11
22 Feb 2023
Abstract
We prove the extended delta conjecture of Haglund, Remmel and Wilson, a combinatorial formula for delta(hl)delta'e(k)e(n)where delta'e(k )and delta(hl )are Macdonald eigenoperators and e(n) is an elementary symmetric function. We actually prove a stronger identity of infinite series of GLm characters expressed in terms of LLT series. This is achieved through new results in the theory of the Schiffmann algebra and its action on the algebra of symmetric functions.
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Details
- Title
- A Proof of the Extended Delta Conjecture
- Publication Details
- FORUM OF MATHEMATICS PI, v 11
- Publisher
- CAMBRIDGE UNIV PRESS; CAMBRIDGE
- Grant note
- JB was supported by NSF grant DMS-1855784 and 2154282. JM was supported by Simons Foundation grant 821999 and NSF grant DMS-2154281. JM and GS were supported by NSF grant DMS-1855804.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Drexel University
- Web of Science ID
- WOS:000937020500001
- Scopus ID
- 2-s2.0-85149126583
- Other Identifier
- 991021861303104721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied