Related papers: The Gamma filtrations for the Spin groups

For any Coxeter group W, we define a filtration of H^*(W;ZW) by W-submodules and then compute the associated graded terms. More generally, if U is a CW complex on which W acts as a reflection group we compute the associated graded terms for…

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite…

Let $\phi:\Z/p\to GL_{n}(\Z)$ denote an integral representation of the cyclic group of prime order $p$. This induces a $\Z/p$-action on the torus $X=\R^{n}/\Z^{n}$. The goal of this paper is to explicitly compute the cohomology groups…

We use recent results proved by Berrick and the author (math.KT/0509404) to improve the periodicity theorem in hermitian K-theory. We define also a new filtration of the classical Witt ring W(A), built from non degenerate quadratic forms…

Let G be a semisimple Lie group with associated symmetric space D, and let Gamma subset G be a cocompact arithmetic group. Let L be a lattice inside a Z Gamma-module arising from a rational finite-dimensional complex representation of G.…

Let $G$ be a complex reductive algebraic group with Lie algebra $\mathfrak{g}$ and let $G_{\mathbb{R}}$ be a real form of $G$ with maximal compact subgroup $K_{\mathbb{R}}$. Associated to $G_{\mathbb{R}}$ is a $K \times…

In this paper we examine the saturation conjecture on decompositions of tensor products of irreducible representations for complex semisimple algebraic groups of type $D$ (the even \emph{spin} groups: Spin$(2n)$ for $n\ge 4$ an integer),…

Let G:=SO(n,1)^\circ and \Gamma be a geometrically finite Zariski dense subgroup with critical exponent delta bigger than (n-1)/2. Under a spectral gap hypothesis on L^2(\Gamma \ G), which is always satisfied for delta>(n-1)/2 for n=2,3 and…

We show that for any compact Lie group $G$ with identity component $N$ and component group $W=G/N$, the category of free rational $G$-spectra is equivalent to the category of torsion modules over the twisted group ring $H^*(BN)[W]$. This…

Let $\Omega$ be a tiling space and let $G$ be the maximal group of rotations which fixes $\Omega$. Then the cohomology of $\Omega$ and $\Omega/G$ are both invariants which give useful geometric information about the tilings in $\Omega$. The…

We describe Universal Coefficient Theorems for the equivariant Kasparov theory for C*-algebras with an action of the group of integers or over a unique path space, using KK-valued invariants. We compare the resulting classification up to…

We give explicit formulas for torus-equivariant fundamental classes of closed $K$-orbits on the flag variety $G/B$ when $G$ is one of the classical groups $SL(n,\C)$, $SO(n,\C)$, or $Sp(2n,\C)$, and $K$ is a symmetric subgroup of $G$. We…

This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…

We initiate the study of real $C^*$-algebras associated to higher-rank graphs $\Lambda$, with a focus on their $K$-theory. Following Kasparov and Evans, we identify a spectral sequence which computes the $\mathcal{CR}$ $K$-theory of…

We investigate the structure of Spin-$G$ bordism groups, focusing on the interplay between Spin and additional twisting symmetries such as $Sp(4)$, $SU(8)$ and $Spin(16)$. Using techniques from spectral sequences, obstruction theory, and…

Let $G$ be the group $SL(2,\mathbb{R})$, $P\subset G$ be the parabolic subgroup of upper triangular matrices and $\Gamma\subset G$ be a cocompact lattice. A right action of $P$ on $\Gamma\backslash G$ defines an orbit foliation…

Let $G = SO_0(2,m),$ the connected component of the Lie group $SO(2,m);\ K = SO(2) \times SO(m),$ a maximal compact subgroup of $G;$ and $\theta$ be the associated Cartan involution of $G.$ Let $X = G/K,\ \frak{g}_0$ be the Lie algebra of…

If $G$ is a compact connected Lie group and $T$ is a maximal torus, we give a wedge decomposition of $\Sigma G/T$ by identifying families of idempotents in cohomology. This is used to give new information on the self-maps of $G/T$.

We give a cellular decomposition of the compact connected Lie group $Spin(7)$. We also determine the L-S categories of $Spin(7)$ and $Spin(8)$.

Let $(A, \mathfrak{m})$ be a Gorenstein local ring, and $\mathcal{F} =\{F_n \}_{n\in \mathbb{Z}}$ a Hilbert filtration. In this paper, we give a criterion for Gorensteinness of the associated graded ring of $\mathcal{F}$ in terms of the…