Related papers: Gaudin Algebras, RSK and Calogero-Moser Cells in T…

The representation theory of rational Cherednik algebras of type A at t=0 gives rise, by considering supports, to a natural family of smooth Lagrangian subvarieties of the Calogero-Moser space. The goal of this article is to make precise…

Using the representation theory of Cherednik algebras at $t=0$ and a Galois covering of the Calogero-Moser space, we define the notions of left, right and two-sided Calogero-Moser cells for any finite complex reflection group. To each…

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of $n$ copies of the universal enveloping algebra $U(\g)$ of a semisimple Lie algebra $\g$. This family is parameterized by collections of pairwise…

Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n. We show that Gaudin subalgebras form a variety isomorphic to the moduli space of stable curves of genus zero…

Using the representation theory of Cherednik algebras at t=0 and a Galois covering of the Calogero-Moser space, we define the notions of left, right and two-sided Calogero-Moser cells for any finite complex reflection group. To each…

We identify the Bethe algebra of the Gaudin model associated to gl(N) acting on a suitable representation with the center of the rational Cherednik algebra and with the algebra of regular functions on the Calogero-Moser space.

Let (W, S) be a Coxeter system. A W-graph is an encoding of a representation of the corresponding Iwahori-Hecke algebra. Especially important examples include the W-graph corresponding to the action of the Iwahori-Hecke algebra on the…

We present a series of algorithms for computing geometric and representation-theoretic invariants of Calogero-Moser spaces and rational Cherednik algebras associated to complex reflection groups. Especially, we are concerned with…

Let $\mathcal{U}$ be a braided tensor category, typically unknown, complicated and in particular non-semisimple. We characterize $\mathcal{U}$ under the assumption that there exists a commutative algebra $A$ in $\mathcal{U}$ with certain…

We introduce and study the family of trigonometric Gaudin subalgebras in $U g^{\otimes n}$ for arbitrary simple Lie algebra $g$. This is the family of commutative subalgebras of maximal possible transcendence degree that serve as a…

Let $G$ be a group acting on a left or right rigid monoidal triangulated category ${\mathbf K}$ which has a Noetherian Balmer spectrum. We prove that the Balmer spectrum of the crossed product category of ${\mathbf K}$ by $G$ is…

The space of $n \times m$ complex matrices can be regarded as an algebraic variety on which the group ${\bf GL}_n \times {\bf GL}_m$ acts. There is a rich interaction between geometry and representation theory in this example. In an…

We construct a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U(g) of a semisimple Lie algebra g. This family is parameterized by collections \mu; z_1,...,z_n, where \mu \in…

Fix a semisimple Lie algebra g. Gaudin algebras are commutative algebras acting on tensor product multiplicity spaces for g-representations. These algebras depend on a parameter which is a point in the Deligne-Mumford moduli space of marked…

As part of the proof of the Bethe ansatz conjecture for the Gaudin model for $\mathfrak{gl}_n$, Mukhin, Tarasov, and Varchenko described a correspondence between inverse Wronskians of polynomials and eigenspaces of the Gaudin Hamiltonians.…

For a finite group $G$, we construct a simplified model for the $G$-symmetric monoidal $G$-$\infty$-category of rational $G$-spectra. Using this model, we classify $\mathcal{I}$-normed algebras in rational $G$-spectra for a given indexing…

We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and soliton equations. Their phase spaces are Jacobian-type bundles over the leaves of a foliation in a…

We introduce the dual affine Robinson-Schensted correspondence that gives a bijection between the extended affine symmetric group and tuples $(\bar{P},\bar{Q},\lambda,N)$, where $\bar{P}$ and $\bar{Q}$ are tabloids, $\lambda$ is a…

We study classical integrable systems based on the Alekseev-Meinrenken dynamical r-matrices corresponding to automorphisms of self-dual Lie algebras, ${\cal G}$. We prove that these r-matrices are uniquely characterized by a non-degeneracy…

We prove the Kazhdan-Lusztig correspondence for a class of vertex operator superalgebras which, via the work of Costello-Gaiotto, arise as boundary VOAs of topological B twist of 3d $\mathcal{N}=4$ abelian gauge theories. This means that we…