Related papers: On highest weight modules over elliptic quantum gr…
Properly specializing the parameters in ``Schnizer modules'', for type A,B,C and D, we get its unique primitive vector. Then we show that the module generated by the primitive vector is an irreducible highest weight module of finite…
In arXiv:1001.2562 a certain non-commutative algebra $A$ was defined starting from a semi-simple algebraic group, so that the derived category of $A$-modules is equivalent to the derived category of coherent sheaves on the Springer (or…
Following our first article, we continue to investigate ultrametic modules over a ring of twisted polynomials of the form $[K;\vfi]$, where $\vfi$ is a ring endomorphism of $K$. The main motivation comes from the the theory of valued…
Let $Q$ be a Dynkin quiver and $\Pi$ the corresponding set of positive roots. For the preprojective algebra $\Lambda$ associated to $Q$ we produce a rigid $\Lambda$-module $I_Q$ with $r=|\Pi|$ pairwise non-isomorphic indecomposable direct…
In this paper, the irreducible modules for the $\mathbb{Z}_{2}$-orbifold vertex operator subalgebra of the parafermion vertex operator algebra associated to the irreducible highest weight modules for the affine Kac-Moody algebra $A_1^{(1)}$…
In this paper, we present a uniform formula of Lusztig's $ \mathbf{a}$-functions on classical Weyl groups. Then we obtain an efficient algorithm for the Gelfand-Kirillov dimensions of simple highest weight modules of classical Lie algebras,…
It is often stated that the Carlitz module is to the ring of univariate polynomials over a finite field what the multiplicative group is to the ring of integers. This analogy extends to the "rank 2" case, where Drinfeld modules play a role…
We announce a systematic way for constructing bispectral algebras of commuting differential operators of any rank N. It enables us to obtain all previously known classes and examples of bispectral operators. Moreover, we give a…
We classify positive energy representations with finite degeneracies of the Lie algebra $W_{1+\infty}\/$ and construct them in terms of representation theory of the Lie algebra $\hatgl ( \infty R_m )\/$ of infinite matrices with finite…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
A brief overview of the recent developments of operadic and higher categorical techniques in algebraic quantum field theory is given. The relevance of such mathematical structures for the description of gauge theories is discussed.
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 discuss highest $\ell$-weight representations of quantum loop algebras and the corresponding functional relations between integrability objects. In particular, we compare the prefundamental and $q$-oscillator representations of the…
Following the previous work, we determine exactly the highest weights for which a tensor product of two induced modules is a tilting module, for the algebraic group $SL_2$ over an algebraically closed field of positive characteristic.
We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective…
We construct explicitly a large family of Gelfand-Tsetlin modules for an arbitrary finite W-algebra of type A and establish their irreducibility. A basis of these modules is formed by the Gelfand-Tsetlin tableaux whose entries satisfy…
Let g be an untwisted affine Kac-Moody algebra and M_J(lambda) a Verma-type module for g with J-highest integral weight lambda. We construct quantum Verma-type modules M_J^q(lambda) over the quantum group U_q(g), investigate their…
Let G be a universal Chevalley group over an algebraically closed field and U^- be the subalgebra of Dist(G) generated by all divided powers X_{\alpha,m} with \alpha<0. We conjecture an algorithm to determine if Fe^+_\omega\ne0, where…
The main idea of this article is simply calculating integer functions in module. The algebraic in the integer modules is studied in completely new style. By a careful construction, a result is proven that two finite numbers is with unequal…
Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$…