A Proof of the Extended Delta Conjecture
We prove the extended delta conjecture of Haglund, Remmel and Wilson, a combinatorial formula for $\Delta _{h_l}\Delta ' _{e_k} e_{n}$ , where $\Delta ' _{e_k}$ and $\Delta _{h_l}$ are Macdonald eigenoperators and $e_n$ is an elementary symmetric function. We act...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508623000033/type/journal_article |
| _version_ | 1811156288603684864 |
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| author | Jonah Blasiak Mark Haiman Jennifer Morse Anna Pun George H. Seelinger |
| author_facet | Jonah Blasiak Mark Haiman Jennifer Morse Anna Pun George H. Seelinger |
| author_sort | Jonah Blasiak |
| collection | DOAJ |
| description | We prove the extended delta conjecture of Haglund, Remmel and Wilson, a combinatorial formula for
$\Delta _{h_l}\Delta ' _{e_k} e_{n}$
, where
$\Delta ' _{e_k}$
and
$\Delta _{h_l}$
are Macdonald eigenoperators and
$e_n$
is an elementary symmetric function. We actually prove a stronger identity of infinite series of
$\operatorname {\mathrm {GL}}_m$
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. |
| first_indexed | 2024-04-10T04:47:59Z |
| format | Article |
| id | doaj.art-28c00e181f8d4383ae1a1bfb84695bd2 |
| institution | Directory Open Access Journal |
| issn | 2050-5086 |
| language | English |
| last_indexed | 2024-04-10T04:47:59Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj.art-28c00e181f8d4383ae1a1bfb84695bd22023-03-09T12:34:19ZengCambridge University PressForum of Mathematics, Pi2050-50862023-01-011110.1017/fmp.2023.3A Proof of the Extended Delta ConjectureJonah Blasiak0Mark Haiman1Jennifer Morse2Anna Pun3https://orcid.org/0000-0001-5279-3936George H. Seelinger4https://orcid.org/0000-0003-3800-3840Dept. of Mathematics, Drexel University, Philadelphia, PA; E-mail:Dept. of Mathematics, University of California, Berkeley, CADept. of Mathematics, University of Virginia, Charlottesville, VA; E-mail:Dept. of Mathematics, CUNY-Baruch College, New York, NY; E-mail:Dept. of Mathematics, University of Michigan, Ann Arbor, MI; E-mail:We prove the extended delta conjecture of Haglund, Remmel and Wilson, a combinatorial formula for $\Delta _{h_l}\Delta ' _{e_k} e_{n}$ , where $\Delta ' _{e_k}$ and $\Delta _{h_l}$ are Macdonald eigenoperators and $e_n$ is an elementary symmetric function. We actually prove a stronger identity of infinite series of $\operatorname {\mathrm {GL}}_m$ 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.https://www.cambridge.org/core/product/identifier/S2050508623000033/type/journal_article05E0516T30 |
| spellingShingle | Jonah Blasiak Mark Haiman Jennifer Morse Anna Pun George H. Seelinger A Proof of the Extended Delta Conjecture Forum of Mathematics, Pi 05E05 16T30 |
| title | A Proof of the Extended Delta Conjecture |
| title_full | A Proof of the Extended Delta Conjecture |
| title_fullStr | A Proof of the Extended Delta Conjecture |
| title_full_unstemmed | A Proof of the Extended Delta Conjecture |
| title_short | A Proof of the Extended Delta Conjecture |
| title_sort | proof of the extended delta conjecture |
| topic | 05E05 16T30 |
| url | https://www.cambridge.org/core/product/identifier/S2050508623000033/type/journal_article |
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