Related papers: Combinatorial Gelfand Models
The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.
Lie symmetry group method is applied to study the Born-Infeld equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra…
Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary.
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
In a recent article we introduced a mechanism for producing a presentation of the descent algebra of the symmetric group as a quiver with relations, the mechanism arising from a new construction of the descent algebra as a homomorphic image…
We present the geometric solutions to some variational problems of statistical mechanics and combinatorics. Together with the Wulff construction, which predicts the shape of the crystals, we discuss the construction which exhibits the shape…
First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth…
We construct a subalgebra of the Hecke algebra of type A. This is a generalization of the group algebra of the alternating groups. All the equivalent classes of irreducible representations of the subalgebra and the q-analogue of the…
In [F. Caselli, Involutory reflection groups and their models, J. Algebra 24 (2010), 370--393] there is constructed a uniform Gelfand model for all non-exceptional irreducible complex reflection groups which are involutory. Such model can…
Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques
We describe an algebra G of diagrams which faithfully gives a diagrammatic representation of the structures of both the Heisenberg-Weyl algebra H - the associative algebra of the creation and annihilation operators of quantum mechanics -…
It is described the group of arrowy permutations (that is extension of symmetric group) and the consequent process of generation of GL(n) and some its subgroups by this combinatoric group and its subgroups.
We describe combinatorial properties of the defining row of a circulant Hadamard matrix by exploiting its orthogonality to subsequent rows, and show how to exclude several particular forms of these matrices.
Gelfand's trick shows that the spherical Hecke algebra of a $p$-adic split reductive group is commutative. We adapt this strategy in order to show that the spherical derived Hecke algebra is graded-commutative under mild assumptions on the…
In \cite{AC12}, among other things, we observed that the structure constants of the Hecke algebra of the Gel'fand pair $(S_{2n},B_n)$ are polynomials in $n$. It is brought to attention by Omar Tout that there is a missing argument in its…
These lectures given in Montreal in Summer 1997 are mainly based on, and form a condensed survey of, the book by N. Chriss and V. Ginzburg: `Representation Theory and Complex Geometry', Birkhauser 1997. Various algebras arising naturally in…
We define combinatorial counterparts to the geometric string vertices of Sen-Zwiebach and Costello-Zwiebach, which are certain closed subsets of the moduli spaces of curves. Our combinatorial vertices contain the same information as the…
We give a combinatorial description (including explicit differential-form bases) for the cohomology groups of the space of n distinct nonzero complex numbers, with coefficients in rank-one local systems which are of finite monodromy around…
This is a survey talk on the study of Gel'fand-Dorfman bialgebras.
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like ``holonomy'', ``parallel transport'', ``bundles'', ``combinatorial curvature'' etc. in the context of simplicial (polyhedral) complexes, posets,…