Related papers: Torus actions, localization and induced representa…

Let $G$ denote a reductive algebraic group over $\mathbb{C}$ and $x$ a nilpotent element of its Lie algebra $\mathfrak{g}$. The Springer variety $\mathcal{B}_x$ is the closed subvariety of the flag variety $\mathcal{B}$ of $G$…

We give a self-contained account of a construction due to Rossmann which lifts Springer's action of a Weyl group on the cohomology of a Springer fiber to an action on its homotopy type. We use this construction to produce a generalization…

If $G$ acts on a $C^*$-correspondence ${\mathcal H}$, then by the universal property $G$ acts on the Cuntz-Pimsner algebra ${\mathcal O}_{\mathcal H}$ and we study the crossed product ${\mathcal O}_{\mathcal H}\rtimes G$ and the fixed point…

The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In this paper, we show that in both situations, the action of…

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…

Let $X$ be a topological space upon which a compact connected Lie group $G$ acts. It is well-known that the equivariant cohomology $H_G^*(X;\Q)$ is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology…

We consider compact homogeneous spaces G/H, where G is a compact connected Lie group and H is its closed connected subgroup of maximal rank. The aim of this paper is to provide an effective computation of the universal toric genus for the…

Let X be a smooth simplicial toric variety. Let Z be the set of T-fixed points of X. We construct a filtration for A(Z), the ring of complex-valued functions on Z, such that Gr A(Z) is isomorphic to the cohomology algebra of X. This is the…

Let $G$ be a compact, connected Lie group and $T \subset G$ a maximal torus. Let $(M,\omega)$ be a monotone closed symplectic manifold equipped with a Hamiltonian action of $G$. We construct a module action of the affine nil-Hecke algebra…

We define the action of a locally compact group $G$ on a topological graph $E$. This action induces a natural action of $G$ on the $C^*$-correspondence ${\mathcal H}(E)$ and on the graph $C^*$-algebra $C^*(E)$. If the action is free and…

Given a simple connected compact Lie group $K$ and a maximal torus $T$ of $K$, the Weyl group $W=N_K(T)/T$ naturally acts on $T$. First, we use the combinatorics of the (extended) affine Weyl group to provide an explicit $W$-equivariant…

We show that two Weyl group actions on the Springer sheaf with arbitrary coefficients, one defined by Fourier transform and one by restriction, agree up to a twist by the sign character. This generalizes a familiar result from the setting…

We describe the action of the Weyl group of a semi simple linear group $G$ on cohomological and K-theoretic invariants of the generalized flag variety $G/B$. We study the automorphism $s_i$, induced by the reflection in the simple root, on…

Let $X$ be a proper algebraic scheme over an algebraically closed field. We assume that a torus $T$ acts on $X$ such that the action has isolated fixed points. The $T$-graph of $X$ can be defined using the fixed points and the one…

Suppose that $(G,T)$ is a second countable locally compact transformation group given by a homomorphism $\ell:G\to\Homeo(T)$, and that $A$ is a separable continuous-trace \cs-algebra with spectrum $T$. An action $\alpha:G\to\Aut(A)$ is said…

We investigate the toric geometry of two families of generalised determinantal varieties arising from permutations: Matrix Schubert varieties ($\overline{X_w}$) and Kazhdan-Lusztig varieties ($\mathcal{N}_{v,w}$). Matrix Schubert varieties…

A polynomial assignment for a continuous action of a compact torus $T$ on a topological space $X$ assigns to each $p\in X$ a polynomial function on the Lie algebra of the isotropy group at $p$ in such a way that a certain compatibility…

Consider the space Hom(Z^n,G) of pairwise commuting n-tuples of elements in a compact Lie group G. This forms a real algebraic variety, which is generally singular. In this paper, we construct a desingularization of the generic component of…

A classical and beautiful story in geometric representation theory is the construction by Springer of an action of the Weyl group on the cohomology of the fibres of the Springer resolution of the nilpotent cone. We establish a natural…

Singular actions on C*-algebras are automorphic group actions on C*-algebras, where the group need not be locally compact, or the action need not be strongly continuous. We study the covariant representation theory of such actions. In the…