Related papers: Formulas of Verlinde type for non-simply connected…

In 1999, Fuchs and Schweigert proposed formulas of Verlinde type for moduli spaces of surface group representations in compact nonsimply connected Lie groups. In this paper, we will prove a symplectic version of their conjecture for…

The main goal of this paper is to obtain a formula for the T-equivariant Riemann-Roch number of certain G-spaces which are the finite dimensional models of certain infinite dimensional spaces with Hamiltonian LG-actions, here T is a maximal…

We prove a decomposition formula for Verlinde sums (rational trigonometric sums), as a discrete counterpart to the Boysal-Vergne decomposition formula for Bernoulli series. Motivated by applications to fixed point formulas in Hamiltonian…

The result contained in this paper is an application of a fixed point formula associated with Hamiltonian loop group action. We obtain a G-space which is a geometric dual of the Verlinde's fusion product. Also we obtain a proof of Verlinde…

In this paper, we examine Lie group actions on moduli spaces (sets themselves built as quotients by group actions) and their fixed points. We show that when the Lie group is compact and connected, we obtain a linear constraint. This…

We give a new proof of Quillen's conjecture for solvable groups via a geometric and explicit method. For p-solvable groups, we provide both a new proof using the Classification of Finite Simple Groups and an asymptotic version without…

We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.

We formulate and prove the Siegel-Weil formula for loop groups.

Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact Lie group…

The purpose of this article is to present a "Groupoid proof" to the Lefschetz fixed point formula for elliptic complexes. We shall define a "relative version" of tangent groupoid, describe the corresponding pseudodifferential calculi and…

We point out that results of Shimizu on internal characters imply a useful non-semisimple variant of the categorical Verlinde formula for factorisable finite tensor categories. When combined with results on pseudo-trace functions by…

Let G be a complex semi-simple group, X a Riemann surface, M_G the moduli space of principal G-bundles on X. When G is simply-connected, there exists a closed formula expressing the dimension of the space H^0(M_G,L) for any line bundle L on…

Verlinde's formula for rational vertex operator algebras computes the fusion rules from the modular transformations of characters. In the non semisimple and non finite case, a logarithmic Verlinde formula has been proposed together with…

We prove a local-to-global result for fixed points of groups acting on affine buildings (possibly non-discrete) of types $\tilde{A}_2$ or $\tilde{C}_2$. In the discrete case, our theorem establishes the corresponding special cases of a…

In joint work with M. Hopkins and C. Teleman we find a new description of the Verlinde algebra associated to a compact Lie group. In this expository account we describe twisted K-theory, prove the theorem for the group SU(2), and motivate…

We prove a multiplicity formula for Riemann-Roch numbers of reductions of Hamiltonian actions of loop groups. This includes as a special case the factorization formula for the quantum dimension of the moduli space of flat connections over a…

The study of fixed point ratios is a classical topic in permutation group theory, with a long history stretching back to the origins of the subject in the 19th century. Fixed point ratios arise naturally in many different contexts, finding…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.

We consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound of the number of fixed points. We also give an obstruction to the existence of…