Cactus groups and Lusztig's asymptotic algebra

Autor: Rouquier, Raphael, White, Noah

We construct a morphism from the cactus group associated with a Coxeter group to the group of invertible elements of Lusztig's asymptotic algebra. This relates to the cactus group action on elements of Coxeter groups defined by Losev and Bonnaf\'e an

Externí odkaz: http://arxiv.org/abs/2408.16922

Labelling Schubert intersections in the Grassmanian

Autor: White, Noah

Points in the intersection of Schubert varieties are counted by various combinatorial objects, for example standard tableaux. This paper consider the problem of producing a natural labelling of intersection points by these combinatorial objects. When

Externí odkaz: http://arxiv.org/abs/1912.10090

The center of the reflection equation algebra via quantum minors

Autor: Jordan, David, White, Noah

We give simple formulas for the elements $c_k$ appearing in a quantum Cayley-Hamilton formula for the reflection equation algebra (REA) associated to the quantum group $U_q(\mathfrak{gl}_N)$, answering a question of Kolb and Stokman. The $c_k$'s are

Externí odkaz: http://arxiv.org/abs/1709.09149

The monodromy of real Bethe vectors for the Gaudin model

Autor: White, Noah

The Bethe algebras for the Gaudin model act on the multiplicity space of tensor products of irreducible $ \mathfrak{gl}_r $-modules and have simple spectrum over real points. This fact is proved by Mukhin, Tarasov and Varchenko who also develop a rel

Externí odkaz: http://arxiv.org/abs/1511.04740

Gaudin Algebras, RSK and Calogero-Moser cells in type A

Autor: Brochier, Adrien, Gordon, Iain, White, Noah

Publikováno v: Brochier, A, Gordon, I G & White, N 2023, ' Gaudin Algebras, RSK and Calogero-Moser cells in type A ', Proceedings of the London Mathematical Society, vol. 126, no. 5, pp. 1467-1495 . https://doi.org/10.1112/plms.12506

We study the spectrum of a family of algebras, the inhomogeneous Gaudin algebras, acting on the $n$-fold tensor representation $\mathbb{C}[x_1, \ldots, x_r]^{\otimes n}$ of the Lie algebra $\mathfrak{gl}_r$. We use the work of Halacheva-Kamnitzer-Ryb

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b6d8f1253266e05c704df03ad7d8373d
https://hdl.handle.net/20.500.11820/c39e62e2-5d45-4c88-97f8-e457e662ef41