Related papers: Fixed point formula and loop group actions

Let K $\subset$ G be compact connected Lie groups with common maximal torus T. Let (M, $\omega$) be a prequantisable compact connected symplectic manifold with a Hamiltonian G-action. Geometric quantisation gives a virtual representation of…

In this article we review the question of constructing geometric quotients of actions of linear algebraic groups on irreducible varieties over algebraically closed fields of characteristic zero, in the spirit of Mumford's geometric…

We present a decomposition of rational twisted $G$-equivariant K-theory, $G$ a finite group, into cyclic group equivariant K-theory groups of fixed point spaces. This generalises the untwisted decomposition by Atiyah and Segal as well as…

Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a theorem stating that more general affine actions of the same…

For a finitely generated free group F_n, of rank at least 2, any finite subgroup of Out(F_n) can be realized as a group of automorphisms of a graph with fundamental group F_n. This result, known as Out(F_n) realization, was proved by…

The generalized Einstein Hilbert action is an extension of the classic scalar curvature energy and Perelman F functional which incorporates a closed three-form. The critical points are known as generalized Ricci solitons, which arise…

We investigate the representation of the symmetric group afforded by the action on its conjugacy class of fixed point free involutions, over an algebraically closed field of finite characteristic p. We discuss the general form of the set of…

We prove a localization formula for group-valued equivariant de Rham cohomology of a compact G-manifold. This formula is a non-trivial generalization of the localization formula of Berline-Vergne and Atiyah-Bott for the usual equivariant de…

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in $\alpha$-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well-known…

In a couple of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In this article, we introduce and examine…

Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra…

We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a…

Let $G/\Gamma$ be the quotient of a semisimple Lie group by an arithmetic lattice. We show that for reductive subgroups $H$ of $G$ that is large enough, the orbits of $H$ on $G/\Gamma$ intersect nontrivially with a fixed compact set. As a…

Let $G$ be a semisimple, simply connected, algebraic group over an algebraically closed field $k$ with Lie algebra $\frak g$. We study the spaces of parahoric subalgebras of a given type containing a fixed nil-elliptic element of $\frak…

Let $T$ be a torus acting on $\CC^n$ in such a way that, for all $1\leq k\leq n$, the induced action on the grassmannian $G(k,n)$ has only isolated fixed points. This paper proposes a natural, elementary, explicit description of the…

As shown by Michel-Ramakrishan (2007) and later generalized by Feigon-Whitehouse (2008), there are "stable" formulas for the average central L-value of the Rankin-Selberg convolutions of some holomorphic forms of fixed even weight and large…

Let $G$ be a compact group, let $\mathcal{B}$ be a unital C$^*$-algebra, and let $(\mathcal{A},G,\alpha)$ be a free C$^*$-dynamical system, in the sense of Ellwood, with fixed point algebra $\mathcal{B}$. We prove that…

First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…

Let T be the circle and A be a T-C*-algebra. Then the T-equivariant K-theory of A is a module over the representation ring of the circle. The latter is a Laurent polynomial ring. Using the support of the module as an invariant, and…

Let H_g denote the closed 3-manifold obtained as the connected sum of g copies of S^2 times S^1, with free fundamental group of rank g. We prove that, for a finite group G acting on H_g which induces a faithful action on the fundamental…