Related papers: Isotropic Schur roots

To a vector space V equipped with a non-quasiclassical involutary solution of the quantum Yang-Baxter equation and a partition $\lambda$, we associate a vector space $\Vl$ and compute its dimension. The functor $V\mapsto \Vl$ is an analogue…

For a finite group action on a finite EI quiver, we construct its `orbifold' quotient EI quiver. The free EI category associated to the quotient EI quiver is equivalent to the skew group category with respect to the given group action.…

Let $A$ be a finite dimensional associative $\mathbb{K}$-algebra over an algebraically closed field $\mathbb{K}$ of characteristic zero. To $A$, we can associate its basic form that is given by a quiver $Q = (Q_0, Q_1)$ with an admissible…

A finite group $G$ is called a Schur group, if any Schur ring over $G$ is associated in a natural way with a subgroup of $Sym(G)$ that contains all right translations. Recently, the authors have completely identified the cyclic Schur…

A fundamental result of Springer says that a quadratic form over a field of characteristic not 2 is isotropic if it is so after an odd degree extension. In this paper we generalize Springer's theorem as follows. Let R be a an arbitrary…

This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting…

We provide an affine cellular structure on the extended affine Hecke algebra and affine $q$-Schur algebra of type $A_{n-1}$ that is defined over $\mathbb{Z}\left[q^{\pm1}\right]$, that is, without an adjoined $q^{\frac{1}{2}}$. This is with…

The irreducible modules over quiver Hecke superalgebras $R_\theta$ can be classified in terms of cuspidal modules. To an indivisible positive root $\alpha$ and a non-negative integer $d$, one associates a quotient $\bar R_{d\alpha}$ of…

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form $<,>$ on…

We introduce the periplectic $q$-Brauer category over an integral domain of characteristic not $2$. This is a strict monoidal supercategory and can be considered as a $q$-analogue of the periplectic Brauer category. We prove that the…

We provide a new proof of the analogue of the Artin-Springer theorem for groups of type $\mathsf{D}$ that can be represented by similitudes over an algebra of Schur index $2$: an anisotropic generalized quadratic form over a quaternion…

We study the essential dimension of representations of a fixed quiver with given dimension vector. We also consider the question of when the genericity property holds, i.e., when essential dimension and generic essential dimension agree. We…

In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…

We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric…

We study the semi-decomposable invariants of a split semisimple group and their extension to a split reductive group by using the torsion in the codimension $2$ Chow groups of a product of Severi-Brauer varieties. In particular, for any…

Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would…

A finite group $G$ is called a Schur group if any $S$-ring over $G$ is associated in a natural way with a subgroup of $Sym(G)$ that contains all right translations. We prove that the groups $\mathbb{Z}_3\times \mathbb{Z}_{3^n}$, where…

Schur rings over the infinite dihedral group $\mathcal{Z}\rtimes\mathcal{Z}_2$ are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over…

The main result of this paper is a recursive description of all decompositions \[ \Delta^+ = \Phi_1 \sqcup \Phi_2 \sqcup \dots \sqcup \Phi_k \] of the positive roots $\Delta^+$ of an arbitrary root system $\Delta$ into a disjoint union of…

We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus $T$ as an ind-object in the category of holomorphic vector bundles on $T$. Extending the results of math.QA/0211262 and math.QA/0308136 we prove that the…