Related papers: Existence of Kirillov--Reshetikhin crystals for mu…

In this paper we develop non-existence results for $m$-ovoids in the classical polar spaces $Q^-(2r+1,q), W(2r-1,q)$ and $H(2r,q^2)$ for $r>2$. In [4] a lower bound on $m$ for the existence of $m$-ovoids of $H(4,q^2)$ is found by using the…

We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical…

We give another proof of the second Rogers-Ramanujan identity by Kashiwara crystals.

We give a new combinatorial model for the crystals of integrable highest weight modules over the classical Lie algebras of type $B$ and $C$ in terms of classical Young tableux. We then obtain a new description of its Littlewood-Richardson…

This paper deals with the fractional Sobolev spaces W^[s,p]. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the…

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1…

We show that an element $w$ of a finite Weyl group $W$ is rationally smooth if and only if the hyperplane arrangement $I$ associated to the inversion set of $w$ is inductively free, and the product $(d_1+1) \cdots (d_l+1)$ of the…

The classification of real Clifford algebras in terms of matrix algebras is well--known. Here we consider the real Clifford algebra ${\mathcal Cl}(r,s)$ not as a matrix algebra, but as a Clifford module over itself. We show that ${\mathcal…

In this paper, we study non-Cohen--Macaulay Buchsbaum Stanley--Reisner rings with linear free resolution. In particular, for given integers $c$, $d$, $q$ with $c \ge 1$, $2 \le q \le d$, we give an upper bound $h_{c,d,q}$ on the dimension…

Let $R=\Bbbk [x_1,..., x_m]$ be a polynomial ring in $m$ variables over $\Bbbk$ with the standard $\mathbb{Z}^m$ grading and $L$ a multigraded Noetherian $R$-module. When $\Bbbk$ is a field, Tchernev has an explicit construction of a…

Let $S$ be a deeply embedded, equicharacteristic, Artinian Gorenstein local ring. We prove that if $R$ is a non-Gorenstein quotient of $S$ of small colength, then every totally reflexive $R$-module is free. Indeed, the second syzygy of the…

We show that certain characteristic varieties of a finitely generated module over a given Weyl algebra arising from weighted degree filtrations are equal to the critical cone of some other characteristic varieties. This behaviour of the…

We show that a ring R has stable range one if and only if every left unit lifts modulo every left principal ideal. We also show that a left quasi-morphic ring has stable range one if and only if it is left uniquely generated. Thus we answer…

We study the crystal of quantum nilpotent subalgebra of $U_q(D_n)$ associated to a maximal Levi subalgebra of type $A_{n-1}$. We show that it has an affine crystal structure of type $D_n^{(1)}$ isomorphic to a limit of perfect…

We apply the method of Gr\"obner-Shirshov bases for replicated algebras developed by Kolesnikov to offer a general approach for constructing free products of trialgebrs (resp. trioids). In particular, the open problem of Zhuchok on…

In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings.…

We obtain an explicit crystal isomorphism between two realizations of crystal bases of finite dimensional irreducible representations of simple Lie algebras of type A and D. The first realization we consider is a geometric construction in…

Let $R$ be a ring and $S$ a multiplicative subset of $R$. We introduce and study the notions of ($u$-)$S$-$w$-Noetherian modules and ($u$-)$S$-$w$-principal ideal modules. Some characterizations of these new concepts are given.

An $(n,r,s)$-system is an $r$-uniform hypergraph on $n$ vertices such that every pair of edges has an intersection of size less than $s$. Using probabilistic arguments, R\"{o}dl and \v{S}i\v{n}ajov\'{a} showed that for all fixed integers…

This paper develops a theory of Besov spaces $\dot{\mathbf{B}}^{\sigma}_{p,q} (N)$ and Triebel-Lizorkin spaces $\dot{\mathbf{F}}^{\sigma}_{p,q} (N)$ on an arbitrary homogeneous group $N$ for the full range of parameters $p, q \in (0,…