Related papers: An algorithm for computing the global basis of an …
In the hyperalgebra $\mathcal{U}_r$ of the $r$-th Frobenius kernel $({\rm SL}_2)_r$ of the algebraic group ${\rm SL}_2$, we construct a basis of the $\mathcal{U}_r$-module generated by a certain element which was given by the author before.…
An algorithm for obtaining all n\times n binary matrices having exactly 2 units in every row and every column is described in the paper. After analysing the work of the algorithm a formula for calculating the number of these matrices has…
We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential…
Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R^m. They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on…
We classify the finite dimensional indecomposable sl(m/n)-modules with at least a typical or singly atypical primitive weight. We do this classification not only for weight modules, but also for generalized weight modules. We obtain that…
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.
The simple integrable modules with finite dimensional weight spaces are classified for the quantum affine special linear superalgebra $\U_q(\hat{\mathfrak{sl}}(M|N))$ at generic $q$. Any such module is shown to be a highest weight or lowest…
Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}(\mathfrak{sl}_n)$ are explicitly constructed using the fusion procedure when $rs^{-1}$ is generic. This provides an alternative and…
We study the decomposition matrices for the unipotent $\ell$-blocks of finite special unitary groups SU$_n(q)$ for unitary primes $\ell$ larger than $n$. Up to very few unknown entries, we give a complete solution for $n=2,\ldots,10$. We…
We consider minimal surfaces of general type with $p_g = 2$, $q = 1$ and $K^2 = 5$. We provide a stratification of the corresponding moduli space and we give some bounds for the number and the dimensions of its irreducible components.
Using the skew-symmetry of the differential operators and multiplication operators in the canonical representations of finite-dimensional classical Lie algebras, we obtain some noncanonical polynomial representations of the classical Lie…
In this paper, we characterized the relationship between Groebner bases and u-bases: any minimal Groebner basis of the syzygy module for n univariate polynomials with respect to the term-over-position monomial order is its u-basis.…
The space of monic centered cubic polynomials with marked critical points is isomorphic to C^2. For each n>0, the locus Sn formed by all polynomials with a specified critical point periodic of exact period n forms an affine algebraic set.…
In this paper, we present an algorithm to compute a basis of the space of algebraic modular forms on the maximal order of the definite quaternion algebra of discriminant $2$, and provide a database of such bases. One of our motivations is…
A simple algorithm to compute all the zeros of a generic polynomial is proposed.
Let $K$ be a finite unramified extension of $\mathbb{Q}_p$, where $p>2$. [CEGS22b] and [EG23] construct a moduli stack of two dimensional mod $p$ representations of the absolute Galois group of $K$. We show that most irreducible components…
A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number…
A class of indecomposable representations of U_q(sl_n) is considered for q an even root of unity (q^h = -1) exhibiting a similar structure as (height h) indecomposable lowest weight Kac-Moody modules associated with a chiral conformal field…
In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional…