Timeline for Identities involving Littlewood–Richardson coefficients?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2023 at 7:48 | comment | added | Ryan Mickler | The culmination of this work, in which Per and I prove some new cases of the Stanley conjecture, is now out: arxiv.org/abs/2309.13870 | |
| Jun 21, 2023 at 2:20 | comment | added | Ryan Mickler | The OP was asked in relation to some new results which have been finally made available here: arxiv.org/abs/2306.11115. In this paper, a relation involving the Jack Littlewood-Richardson coefficients of the following form is shown $\sum_{\gamma \supset \mu \cup \nu} c_{\mu\nu}^{\gamma}(\alpha) f_{\gamma,\mu,\nu}(u) = g_{\mu,\nu}(u)$, where $f_{\gamma,\mu,\nu}(u)$ and $g_{\mu,\nu}(u)$ are explict rational functions in a variable $u$. | |
| Aug 1, 2022 at 19:29 | history | edited | LSpice | CC BY-SA 4.0 |
Name of HW reference
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| Aug 1, 2022 at 18:48 | answer | added | Igor Pak | timeline score: 4 | |
| Jul 31, 2022 at 0:55 | comment | added | Richard Stanley | For a mild generalization of the Harris-Willenbring identity, see Problem 92(d) at math.mit.edu/~rstan/ec/ch7supp.pdf. Problem 91 also has some identities involving $c^\lambda_{\mu\nu}$ together with $f^\lambda$, $f^\mu$, and $f^\nu$. | |
| Jul 30, 2022 at 21:01 | comment | added | darij grinberg | For another example: arxiv.org/abs/2008.06128 | |
| Jul 30, 2022 at 19:47 | comment | added | Sam Hopkins | There are other identities involving LR coefficients which follow from exceptional equalities among skew Schur functions (see e.g. arxiv.org/abs/math/0602634) or sums of products of pairs of Schur functions (see e.g. arxiv.org/abs/math/0004113), but these are of a different flavor. | |
| Jul 30, 2022 at 19:37 | comment | added | Sam Hopkins | You can take the definition of the LR coefficients $s_{\mu}(x_1,\ldots) s_{\nu}(x_1,\ldots) = \sum_{\lambda} c^{\lambda}_{\mu, \nu} s_{\lambda}(x_1,\ldots)$ and do any of the several nice specializations of Schur functions to get such an identity. | |
| Jul 30, 2022 at 19:33 | history | asked | Per Alexandersson | CC BY-SA 4.0 |