Related papers: Cohomology at infinity and the well-rounded retrac…

Let $V$ be a finite-dimensional unitary representation of a compact quantum group $\mathrm{G}$ and denote by $\mathrm{G}_W$ the isotropy subgroup of a linear subspace $W\le V$ regarded as a point in the Grassmannian $\mathbb{G}(V)$. We show…

Let X be a homogeneous space, X = G/H, where G is a connected linear algebraic group over a number field k, and H is a k-subgroup of G (not necessarily connected). Let S be a finite set of places of k. We compute the Brauer-Manin…

We prove that if $\Gamma$ is a lattice in the group of isometries of a symmetric space of non-compact type without euclidean factors, then the virtual cohomological dimension of $\Gamma$ equals its proper geometric dimension.

Let $\Gamma$ be a finite d-valent graph and G an n-dimensional torus. An ``action'' of G on $\Gamma$ is defined by a map, $\alpha$, which assigns to each oriented edge e of $\Gamma$ a one-dimensional representation of G (or, alternatively,…

Real forms of a complex reductive group are classified in terms of Galois cohomology $H^1(\Gamma,G_{ad})$ where $G_{ad}$ is the adjoint group. Alternatively, the theory of the Cartan involution gives a description in terms of cohomology…

The Coleman-Mandula (CM) theorem states that the Poincar\'e and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field…

We study the space of irreducible representations of a crossed product C*-algebra AxG, where G is a finite group. We construct a space $\Gamma$ which consists of pairs of irreducible representations of A and irreducible projective…

Let $G$ be a simply connected, almost simple group over an algebraically closed field $\mathbf k$, and $P$ a maximal parabolic subgroup corresponding to omitting a cominuscule root. We construct a compactification $\phi:T^*G/P\rightarrow…

Let $\Gamma$ be a weakly irreducible higher rank lattice. In this paper, we will prove various rigidity results for the $\Gamma$-action following a philosophy of the Zimmer program. We provide new rigidity results including local and global…

Let $X$ be a smooth projective curve over a field $k$ with an action of a finite group $G$. A well-known result of Chevalley and Weil describes the $k[G]$-module structure of cohomologies of $X$ in the case when the characteristic of $k$…

We prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$…

Let $\mathfrak{g}$ be an untwisted affine Lie algebra with associated Weyl group $W_a$. To any level 0 weight $\gamma$ we associate a weighted graph $\Gamma_\gamma$ that encodes the orbit of $\gamma$ under the action $W_a$. We show that the…

To each complex reflection group $\Gamma$ one can attach a canonical symplectic singularity $\mathcal{M}_\Gamma$ arXiv:math/9903070. Motivated by the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and Rastelli…

For a compact real form $U$ of a complex simple Lie group $G$, and an irreducible representation $\rho:\Gamma \to U$ of a Fuchsian group of the first kind $\Gamma$, it is shown that the classical isomorphism of Shimura, for the periods of a…

We consider the moduli space ${\cal M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a semisimple complex Lie group, and study the action of a finite group $\Gamma$ on ${\cal M}(G)$ induced by a holomorphic…

We explore the connection between super $\mathcal{W}$-algebras ($\mathcal{SW}$-algebras) and $\mathrm{G}$-structures with torsion. The former are realised as symmetry algebras of strings with $\mathcal{N}=(1,0)$ supersymmetry on the…

We compute the cyclic homology for the cross-product al- gebra $A(M)\rtimes\Gamma$ of the algebra of complete symbols on a compact man- ifold $M$ with action of a finite group $\Gamma$. A spectral sequence argument shows that these groups…

Let $K$ be a global function field of characteristic $p$, and let $\Gamma$ be a finite-index subgroup of an arithmetic group defined with respect to $K$ and such that any torsion element of $\Gamma$ is a $p$-torsion element. We define…

We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\Gamma$. Under favorable conditions, the cohomology is freely generated in a single degree over this graded…

Let $N>1$ be an integer, and let $\Gamma = \Gamma_0 (N) \subset \SL_4 (\Z)$ be the subgroup of matrices with bottom row congruent to $(0,0,0,*)\mod N$. We compute $H^5 (\Gamma; \C) $ for a range of $N$, and compute the action of some Hecke…