相关论文: New singular Gelfand-Tsetlin $\mathfrak{gl} (n)$-m…

We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all…

We define and study the Kirillov--Reshetikhin modules for algebras of type $G_2$. We compute the graded character of these modules and verify that they are in accordance with the conjectures in math.QA/981202 and math.QA/0102113. These…

We classify blocks in the BGG category $\mathcal O$ of modules of non-integral weights for the exceptional Lie superalgebra $G(3)$. We compute the characters for tilting modules of non-integral weights in $\mathcal O$. Reduction methods are…

In this note we are interested in labelling the irreducible representations of non-semisimple specialisations of Hecke algebras of complex reflection groups. We will use category O for the rational Cherednik algebra and the KZ functor…

The new approach to the theory of complex representrations of the finite symmetric groups which based on the notions of Coxeter generators., Gelfand-Zetlin algebras, Hecke algebra, Young-Jucys-Murphi generators and which hardly used…

We construct special cycles on the moduli stack of unitary shtukas. We prove an identity between (1) the r-th central derivative of non-singular Fourier coefficients of a normalized Siegel--Eisenstein series, and (2) the degree of special…

We generalise some well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs. This leads to a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coefficients of…

We describe the category of integrable sl(1|n)^ -modules with the positive central charge and show that the irreducible modules provide the full set of irreducible representations for the corresponding simple vertex algebra.

We formulate the general construction for singular vectors in Verma modules of the affine sl(2|1) superalgebra. We then construct sl(2|1) representations out of the fields of the non-critical N=2 string. This allows us to extend naturally…

Following a question of Vinberg, a general method to construct monomial bases for finite-dimensional irreducible representations of a reductive Lie algebra was developed in a series of papers by Feigin, Fourier, and Littelmann. Relying on…

A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand--Tsetlin patterns. Explicit formulas for the matrix elements…

We study versions of strict Mittag-Leffler modules relativized to a class $\cK$ (of modules), that is, \emph{strict} versions (in the technical sense of Raynaud and Gruson) of $\cK$-Mittag-Leffler modules, as investigated in the preceding…

By some SL(2, Z) modular forms introduced in [4] and [10], we construct some modular forms over SL2(Z) and some modular forms over {\Gamma}^0(2) and {\Gamma}_0(2) in odd dimensions. In parallel, we obtain some new cancellation formulas for…

Let $\Delta= \sum_{m=0}^\infty q^{(2m+1)^2} \in \mathbb{F}_2[[q]]$ be the reduction mod 2 of the $\Delta$ series. A modular form $f$ modulo $2$ of level 1 is a polynomial in $\Delta$. If $p$ is an odd prime, then the Hecke operator $T_p$…

We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated…

In 1994, Kac and Wakimoto suggested a generalization of Bernstein and Leites character formula for basic Lie superalgebras, and the natural question was raised: to which simple highest weight modules does it apply? In this paper, we prove a…

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of $n$ copies of the universal enveloping algebra $U(\g)$ of a semisimple Lie algebra $\g$. This family is parameterized by collections of pairwise…

In this paper, we prove that the class of all special Gelfand--Dorfman algebras (GD-algebras) is closed with respect to homomorphisms and thus forms a variety. We also prove that every 2-dimensional GD-algebra is special. For the latter, we…

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…

We develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras: the Baer modules, and the Mittag-Leffler ones.