Related papers: The symplectic ideal and a double centraliser theo…

Let $K$ be an arbitrary field of characteristic not equal to 2. Let $m, n\in\N$ and $V$ an $m$ dimensional orthogonal space over $K$. There is a right action of the Brauer algebra $\bb_n(m)$ on the $n$-tensor space $V^{\otimes n}$ which…

We compute the irreducible constitutents of the product of the Weil character and the Steinberg character in those finite classical groups for which a Weil character is defined, namely the symplectic, unitary and general linear groups. It…

We consider the coordinate ring of a hyperelliptic curve and let $\mathfrak{g}\otimes R$ be the corresponding current Lie algebra where $\mathfrak g$ is a finite dimensional simple Lie algebra defined over $\mathbb C$. We give a generator…

We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by…

We prove that, for nice classes of infinite-dimensional smooth groups G, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of G. This yields a bridge between infinite-dimensional…

We investigate a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifolds defined by Ismagilov, Losik, and Michor and investigate its properties. We provide both vanishing and non-vanishing results and…

Let $R$ be a regular ring of dimension $d$ and $L$ be a $c$-divisible monoid. If ${K}_1{Sp}(R)$ is trivial and $k \geq d+2,$ then we prove that the symplectic group ${Sp}_{2k}(R[L])$ is generated by elementary symplectic matrices over…

We generalize some results of Greither and Popescu to a geometric Galois cover $X\rightarrow Y$ which appears naturally for example in extensions generated by $\mathfrak{p}^n$-torsion points of a rank 1 normalized Drinfeld module (i.e. in…

Analogs of the classical Sylvester theorem have been known for matrices with entries in noncommutative algebras including the quantized algebra of functions on GL(N) and the Yangian for gl(N). We prove a version of this theorem for the…

Given a compact Lie group $G$ acting on a space $X$, the classical Atiyah-Segal completion theorem identifies topological $K$-theory of the homotopy quotient $X/G$ with an explicit completion of $G$-equivariant topological $K$-theory of…

Let A be a commutative ring, and let \a be a weakly proregular ideal in A. (If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category of cohomologically \a-torsion complexes. We prove…

Given an affine Poisson algebra, that is singular one may ask whether there is an associated symplectic form. In the smooth case the answer is obvious: for the symplectic form to exist the Poisson tensor has to be invertible. In the…

We construct a perfect version of Morel--Voevodsky's motivic homotopy category over a perfect base scheme in positive characteristic. By checking the axioms of a coefficient system, we establish a six-functor formalism. We show that…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in…

We observe that all classical Hamiltonian systems coming from the invariant polynomials on a reductive Lie algebra g can be integrated in a universal way. This is a consequence of Ng\^o's action of the group scheme J of regular centralizers…

Let $p$ be a prime number, $\Bbbk$ a field of characteristic $p$ and $G$ a finite $p$-group. Let $V$ be a finite-dimensional linear representation of $G$ over $\Bbbk$. Write $S = \mathrm{Sym} V^*$. For a class of $p$-groups which we call…

We prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V_p(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of…

Let w be an elliptic element of the Weyl group of a connected reductive group G. Let X be the set of pairs (g,B) where g is an element of G, B is a Borel subgroup of G and B,gBg^{-1} are in relative position w. Then G acts naturally on X.…

We prove Clifford theoretic results on the representations of finite groups which only hold in characteristic $2$. Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $\varphi$ be an irreducible $2$-Brauer character of…