相关论文: A twining character formula for Demazure modules (…

In this paper we aim to generalize the results in Baier and Zhao and develop a general formula for large sieve with characters to powerful moduli that will be an improvement to the result of Zhao.

We give a parametrization for crystal bases of Demazure modules as a set of lattice points in some convex polytope and we also describe explicitly the extremal vectors as solutions of some system of linear equations.

The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.

Earlier we presented a method to decompose modal formulas for processes with the internal action $\tau$, and congruence formats for branching and $\eta$-bisimilarity were derived on the basis of this decomposition method. The idea is that a…

We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…

We give a simple proof for the reciprocity formulas of character Dedekind sums associated with two primitive characters, whose modulus need not to be same, by utilizing the character analogue of the Euler-MacLaurin summation formula.…

This article present a new, direct and simple formula for constructing Mignotte sequences.

The weights of finite-dimensional representations of simple Lie algebras are naturally associated with Weyl polytopes. Representation characters decompose into multiplicity-free sums over the weights in Weyl polytopes. The Brion formula for…

We construct a supercharacter theory for the group of invertible elements of a reduced algebra. For the case of the triangular group, we obtain the formula for values of supercharacters on superclasses.

We study properties of ramification in Iwasawa modules.

The character formula of any finite dimensional irreducible module for Lie superalgebra $\mathfrak{osp}(3|2m)$ is obtained in terms of characters of generalized Verma modules.

In this article, we generalize the concept of torsion pairs and study its structure. As a trial of obtaining all torsion pairs, we decompose torsion pairs by projective modules and injective modules. Then we calculate torsion pairs on the…

In this paper we study a family of finite-dimensional graded representations of the current algebra of $\mathfrak{sl}_2$ which are indexed by partitions. We show that these representations admit a flag where the successive quotients are…

We propose upper bounds for the number of modular constituents of the restriction modulo $p$ of a complex irreducible character of a finite group, and for its decomposition numbers, in certain cases.

We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…

We describe a cluster algebra algorithm for calculating q-characters of Kirillov-Reshetikhin modules for any untwisted quantum affine algebra. This yields a geometric q-character formula for tensor products of Kirillov-Reshetikhin modules.…

We study finite-dimensional respresentations of twisted current algebras and show that any graded twisted Weyl module is isomorphic to level one Demazure module for the twisted affine Kac-Moody algebra. Using the tensor product property of…

We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…

In this paper, We use the Fourier series expansion of real variables function, We give a formula to calculate the Dirichlet character sum, and four special examples are given.

We consider a sequence of composite bivariate Bernstein operators and the cubature formula associated with them. The upper bounds for the remainder term of the cubature formula are described in terms of moduli of continuity of order two.…