相关论文: Calogero-Moser space and Kostka polynomials

We give some classes of power maps with low $c$-differential uniformity over finite fields of odd characteristic, {for $c=-1$}. Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect $c$-nonlinear…

A classical result of Sherman says that if the space of self-adjoint elements in a $C^*$-algebra $\mathcal{A}$ is a lattice with respect to its canonical order, then $\mathcal{A}$ is commutative. We give a new proof of this theorem which…

The space of m-harmonic polynomials related to a Coxeter group G and a multiplicity function m on its root system is defined as the joint kernel of the properly gauged invariant integrals of the corresponding generalised quantum…

We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question…

We show that the group of all holomorphic automorphisms of complex affine space $\mathbb C^n$, $n>1$, and several of its subgroups satisfy the parametric Oka property with approximation and with interpolation on discrete sets.

We extend fundamental inequalities related to the canonical map of surfaces of general type to positive characteristic. Next, we classify surfaces on the Noether lines, i.e., even and odd Horikawa surfaces, in positive characteristic. We…

We apply a method inspired by Popa's intertwining-by-bimodules technique to investigate inner conjugacy of MASAs in graph $C^*$-algebras. First we give a new proof of non-inner conjugacy of the diagonal MASA ${\mathcal D}_n$ to its…

We consider the $C^*$-algebra generated by finitely many annihilation operators acting on the weakly monotone Fock space, and we call it weakly monotone $C^*$-algebra. We give an abstract representation for this algebra, showing that it is…

We describe an algorithm computing the monodromy and the pole order filtration on the Milnor fiber cohomology of any reduced projective plane curve $C$. The relation to the zero set of Bernstein-Sato polynomial of the defining homogeneous…

We study multiple chordal SLE$(\kappa)$ systems in a simply connected domain $\Omega$, where $z_1, \ldots, z_n \in \partial \Omega$ are boundary starting points and $q \in \partial \Omega$ is an additional marked boundary point. As a…

A natural star product for 4-d $\kappa$-Minkowski space is used to investigate various classes of $\kappa$-Poincar\'e invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual $\phi^4$…

Each degree $n$ polynomial in one variable of the form $(x+1)(x^{n-1}+c_1x^{n-2}+\cdots +c_{n-1})$ is representable in a unique way as a Schur-Szeg\H{o} composition of $n-1$ polynomials of the form $(x+1)^{n-1}(x+a_i)$, see \cite{Ko1},…

Let $G$ be a reductive group. We prove that a family of polynomial actions of $G$ on $\mathbb{C}^2$, holomorphically parametrized by an open Riemann surface, is linearizable. As an application, we show that a particular class of reductive…

We say a completely positive contractive map between two C*-algebras has order zero, if it sends orthogonal elements to orthogonal elements. We prove a structure theorem for such maps. As a consequence, order zero maps are in one-to-one…

In an earlier paper [1] it was shown that the Frobenius compound characters for the symmetric groups are related to the irreducible characters by a linear relation that involves a unitriagular coupling matrix that gives the Frobenius…

We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases: (i) F is an algebraically closed field of characteristic…

In this note we consider the Milnor fiber $F$ associated to a reduced projective plane curve $C$. A computational approach for the determination of the characteristic polynomial of the monodromy action on the first cohomology group of $F$,…

In this paper we study the structure of the $C^*$-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic $C^*$-algebras over this poset. We construct the extensions…

From a planar algebra, we give a functorial construction to produce numerous associated $C^*$-algebras. Our main construction is a Hilbert $C^*$-bimodule with a canonical real subspace which produces Pimsner-Toeplitz, Cuntz-Pimsner, and…

A canonical cover generalizing the left Fischer cover to arbitrary sofic shifts is introduced and used to prove that the left Krieger cover and the past set cover of a sofic shift can be divided into natural layers. These results are used…