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: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
|
| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508623000033/type/journal_article |
| Summary: | 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. |
|---|---|
| ISSN: | 2050-5086 |