Related papers: On the one-dimensional representations of the gene…

Let $K/F$ be a quadratic extension of $p$-adic fields, and $n$ a positive integer. A smooth irreducible representation of the group $GL(n,K)$ is said to be distinguished, if it admits on its space a nonzero $GL(n,F)$-invariant linear form.…

The representation dimension of a finite group $G$ is the minimal dimension of a faithful complex linear representation of $G$. We prove that the representation dimension of any finite group $G$ is at most $\sqrt{|G|}$ except if $G$ is a…

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

We prove that the numbers of irreducible n-dimensional complex continuous representations of the special linear groups over p-adic integers grow slower than the square of n. We deduce that the abscissas of convergence of the representation…

Let $G$ be a connected reductive group over $\kk$, an algebraic closure of a finite field. For an integer $r\ge 1$ let $G_r=G(\kk[\e]/(\e^r))$ viewed as an algebraic group of dimension $r\dim G$ over $\kk$. We show that the character of the…

Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.

For weighted group convoltion measure algebra we construct a representation on reflexsive space.

Let $F$ be an infinite division ring, $V$ be a left $F$-vector space, $r>0$ be an integer. We study the structure of the representation of the linear group $\mathrm{GL}_F(V)$ in the vector space of formal finite linear combinations of…

We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made…

We provide a characterization of the finite dimensionality of vector spaces in terms of the right-sided invertibility of linear operators on them.

We characterize unitary representations of braid groups $B_n$ of degree linear in $n$ and finite images of such representations of degree exponential in $n$.

We list the irreducible two dimensional complex representations of the Braid group B3 in elementary way. Then, we make a decomposition of the square of its irreducible Burau representation.

The aim of this work is to give a combinatorial way to describe all irreducible representations in case the super-dimension of $V$ is $(3|1)$.

Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…

Let $Y_{1|1}$ be the Yangian associated to the general linear Lie superalgebra $\mathfrak{gl}_{1|1}$, defined over an algebraically closed field $\mathbbm{k}$ of characteristic $p>2$. In this paper, we classify the finite dimensional…

The new extensions of the Poincar\'e superalgebra recently found in ten and eleven dimensions are shown to admit a linear realization. The generators of the nonlinear and linear group transformations are shown to fall into equivalent…

We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic…

We prove a characterization of monomial projective representations of finitely generated nilpotent groups. We also characterize polycyclic groups whose projective representations are finite dimensional.

The representation category $\mathcal{A} = Rep(G,\epsilon)$ of a supergroup scheme $G$ has a largest proper tensor ideal, the ideal $\mathcal{N}$ of negligible morphisms. If we divide $\mathcal{A}$ by $\mathcal{N}$ we get the semisimple…

We found another N=1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N=1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex…