Related papers: The Brauer algebra and the symplectic Schur algebr…

A new basis of the $q$-Brauer algebra is introduced, which is a lift of Murphy bases of Hecke algebras of symmetric groups. This basis is a cellular basis in the sense of Graham and Lehrer. Subsequently, using combinatorial language we…

By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a…

This paper introduces the notion of Brauer-friendly modules, a generalisation of endo-p-permutation modules. A module over a block algebra OGe is said to be Brauer-friendly if it is a direct sum of indecomposable modules with compatible…

In this project, we will study the Brauer group that was first defined by R. Brauer. The elements of the Brauer group are the equivalence classes of finite dimensional central simple algebra. Therefore understanding the structure of the…

In this article, we compute both the algebraic and the analytic Brauer groups of a homogeneous space under the action of a connected, simply connected, semisimple complex algebraic group, where the stabilizer subgroup is closed and…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi-Trudi formula and the Lascoux-Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of…

Brauer algebras form a tower of cellular algebras. There is a well-defined notion of limiting blocks for these algebras. In this paper we give a complete description of these limiting blocks over any field of positive characteristic. We…

We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like `local' objects, which…

We prove the little Grothendieck theorem for any 2-convex noncommutative symmetric space. Let $\M$ be a von Neumann algebra equipped with a normal faithful semifinite trace $\t$, and let $E$ be an r.i. space on $(0, \8)$. Let $E(\M)$ be the…

We establish a rather unexpected and simple criterion for the boundedness of Schur multipliers $S_M$ on Schatten $p$-classes which solves a conjecture proposed by Mikael de la Salle. Given $1 < p < \infty$, a simple form our main result…

The plethysm product of Schur functions corresponds to composing polynomial representations of infinite general linear groups. Finding the plethysm coefficients $\langle s_\nu \circ s_\mu, s_\lambda\rangle$ that express an arbitrary…

By considering the specialisation $s_{\lambda}(1,q,q^2,...,q^{n-1})$ of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape $\lambda$ in terms of two properties of the boxes in…

Let $K$ be a number field, and let $\mathcal{X}$ be a proper regular flat scheme over $\mathcal{O}_{K}$ with a generic fiber $X$ geometrically connected over $K$. We prove that there is an exact sequence up to finite groups $0\rightarrow…

The gauge invariant degrees of freedom of matrix models based on an N x N complex matrix, with U(N) gauge symmetry, contain hidden free particle structures. These are exhibited using triangular matrix variables via the Schur decomposition.…

Two number fields are said to be Brauer equivalent if there is an isomorphism between their Brauer groups that commutes with restriction. In this paper we prove a variety of number theoretic results about Brauer equivalent number fields…

When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form. A number of q-analogues…

For $k\ge 1$, the homogeneous symmetric functions $G(k,m)$ of degree $m$ defined by $\sum_{m\ge 0} G(k,m) z^m=\prod_{i\ge 1} \big(1+x_iz+x^2_iz^2+\cdots+x^{k-1}_iz^{k-1}\big)$ are called \emph{Petrie symmetric functions}. As derived by…

We establish new Murnaghan--Nakayama rules for symplectic, orthogonal and orthosymplectic Schur functions. The classical Murnaghan--Nakayama rule expresses the product of a power sum symmetric function with a Schur function as a linear…

We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the conjugated classes of finite permutations…