Related papers: Weyl group actions on the Springer sheaf

We construct a Stratonovich-Weyl correspondence for each generic representation of a Heisenberg motion group by using the Weyl calculus on the Fock space.

In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms of sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight is non-positive, which…

We give an apriori description of a set of irreducible representations of a Weyl group which parametrize the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre…

We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau…

This paper provides sufficient conditions for the boundedness of Weyl operators on modulation spaces. The Weyl symbols belong to Wiener amalgam spaces, or generalized modulation spaces, as recently renamed by their inventor Hans…

We solve the noncommutative Noether's problem for the reflection groups by showing that the skew field of the invariants of the Weyl algebra under the action of any reection group is a Weyl field, that is isomorphic to a skew field of some…

Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the $L^2$ behavior of a Fourier…

When it is based on Kac-Peterson form of Affine Weyl Groups, Weyl-Kac character formula could be formulated in terms of Theta functions and a sum over finite Weyl groups. We, instead, give a reformulation in terms of Schur functions which…

Let $W$ be a reflection group in a plane and $P$ a rational polygon that is invariant under the $W$-action. The action of $W$ on $P$ induces a $W$-action on the toric variety $X_P$ associated with $P$. In this paper, we study the…

We consider the coadjoint action of a Loop group of a compact group on the dual of the corresponding centrally extended Loop algebra and prove that a Brownian motion in a Cartan subalgebra conditioned to remain in an affine Weyl chamber -…

In this article, we investigate Hopf actions on vertex algebras. Our first main result is that every finite-dimensional Hopf algebra that inner faithfully acts on a given \pi_2-injective vertex algebra must be a group algebra. Secondly,…

We define a monoidal category $\operatorname{\mathbf{W}}$ and a closely related 2-category $\operatorname{\mathbf{2Weyl}}$ using diagrammatic methods. We show that $\operatorname{\mathbf{2Weyl}}$ acts on the category $\mathbf{TL}…

In a previous article we have defined an action of the Iwahori-Hecke algebra of a Coxeter group W on a free module with basis indexed by the involutions in W. In this paper we show that the specialization of this action at the parameter 0…

In this paper we give an extensive description of Weyl quadratic gravity as the gauge theory of the Weyl group. The previously discovered (vectorial) torsion/non-metricity equivalence is shown to be built-in as it corresponds to a…

Let G be a simple algebraic group over C with the Weyl group W. For a unipotent element u of G, let B_u be the variety of Borel subgroups of G containing u. Let L be a Levi subgroup of a parabolic subgroup of G with the Weyl subgroup W_L.…

We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features…

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set…

We show that signs of Fourier coefficients, on certain sub-families, determine the half-integral weight cuspidal eigenform uniquely, up to a positive constant. We also study sign change results for the product of the Fourier coefficients of…

Let $G$ be a simple complex Lie group with Weyl group $W$. We give a formula for the character of $W$ on the zero weight space of any finite dimensional representation of $G$. The formula involves partition functions, generalizing Kostant's…

One can associate an invariant to a large class of regular codimension two defects of the six dimensional $(0,2)$ SCFT $\mathscr{X}[j]$ using the classical Springer correspondence. Such an association allows a simple description of…