相关论文: Invariants of mixed representations of quivers II …
We consider quiver representations respecting a quiver automorphism and show that the dimension vectors of the indecomposables are precisely the positive roots of an associated symmetrisable Kac-Moody Lie algebra. Moreover, every such Lie…
We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras.
In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.
We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…
Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be recovered from the data of the corresponding…
For the family of the orthogonal quantum matrix algebras we investigate the structure of their characteristic subalgebras -- special commutative subalgebras, which for the subfamily of the reflection equation algebras appear to be central.…
We consider birack and switch colorings of braids. We define a switch structure on the set of permutation representations of the braid group and consider when such a representation is a switch automorphism. We define quiver-valued…
In this paper we study of *-representations for polynomial algebras on quantum matrix spaces. We deal with two special cases of the polynomial algebras, namely the algebra of polynomials on quantum complex matrices $\mathrm{Mat_2}$ and on…
A regular factor is a factor algebra of the unitriangular Lie algebra with respect to some regular ideal. In the paper we construct system of generators of the field of invariants for the coadjoint representation of an arbitrary regular…
The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the representation theory of quantum groups. The first part of…
We give a new technique for constructing presentations by generators and relations for representations of groups like $SL_n(\mathbb{Z})$ and $Sp_{2g}(\mathbb{Z})$. Our results play an important role in recent work of the authors calculating…
The metohod of ortogonal rotations introduced in the previous papers of the author is used for construction of the explicit form the generators of the simple roots for quantum (and ussual) semisimple algebras. All calculations are presented…
We discuss some new invariants of quark mixing and show their usefulness with a simple example. We also present some other new tools for analyzing quark mixing.
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
We find a minimal set of generators for the coordinate ring of Calogero-Moser space $\mathcal{C}_3$ and the algebraic relations among them explicitly. We give a new presentation for the algebra of $3\times3$ invariant matrices involving the…
By analogy with the real and complex affine groups, whose unitary irreducible representations are used to define the one and two-dimensional continuous wavelet transforms, we study here the quaternionic affine group and construct its…
We prove a new formula for the generating function of polynomials counting absolutely stable representations of quivers over finite fields. The case of irreducible representations is studied in more detail.
We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface into the symplectic group.
We change the definition of the vertex representations. As a result the vertex representations has one parameter.