相关论文: Bases for local Weyl modules for the hyper and tru…
For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…
It was recently shown that gl^(1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the…
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require…
We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing dual Coxeter number,…
The paper presents a construction of finite-dimensional irreducible representations of the Lie algebra $\mathfrak{g}_2$. The representation space is constructed as the space of solutions to a certain system of partial differential equations…
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…
We identify level one global Weyl modules for toroidal Lie algebras with certain twists of modules constructed by Moody-Eswara Rao-Yokonuma via vertex operators for type ADE and by Iohara-Saito-Wakimoto and Eswara Rao for general type. The…
According to Kirillov's theory, the construction of a unitary irreducible representation of a nilpotent Lie group requires a precise computation of some polarizing subalgebra subordinated to a linear functional in the linear dual of the…
We construct characteristic-free bases and BGG resolutions of unitary simple modules of quiver Hecke algebras and Cherednik algebras. We hence solve and vastly generalise Berkesch-Griffeth-Sam's conjecture, calculate the Castelnuovo-Mumford…
In this paper we present a systematic study of $W$ algebras from the Hamiltonian reduction point of view. The Drinfeld-Sokolov (DS) reduction scheme is generalized to arbitrary $sl_2$ embeddings thus showing that a large class of W algebras…
A conservative extension of general relativity by integrable Weyl geometry is formulated, and a new class of cosmological models ({\em Weyl universes}) is introduced and studied. A short discussion of how these new models behave in the…
We compute the Yoneda extension algebra of the collection of Weyl modules for $GL_2$ over an algebraically closed field of positive characteristic p by developing a theory of generalised Koszul duality for certain 2-functors, one of which…
We describe a basis for free Lie superalgebras which uses the theory of basic commutators. The only description for bases for free Lie superalgebras that I have found in the literature is in the book "Infinite dimensional Lie superalgebras"…
We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the…
Equivariant twisted K theory classes on compact Lie groups $G$ can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra $LG$…
In this article, we provide a comprehensive characterization of invariants of classical Lie superalgebras from the super-analog of the Schur-Weyl duality in a unified way. We establish $\mathfrak{g}$-invariants of the tensor algebra…
We investigate Whittaker modules for generalized Weyl algebras, a class of associative algebras which includes the quantum plane, Weyl algebras, the universal enveloping algebra of sl_2 and of Heisenberg Lie algebras, Smith's…
In this paper we construct combinatorial bases of Feigin-Stoyanovsky's type subspaces of standard modules for level $k$ affine Lie algebra $C_\ell^{(1)}$. We prove spanning by using annihilating field $x_\theta (z)^{k+1}$ of standard…
Given a suitable ordering of the positive root system associated with a semisimple Lie algebra, there exists a natural correspondence between Verma modules and related polynomial algebras. With this, the Lie algebra action on a Verma module…
This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps $\alpha : E \rightarrow F$ which, for smooth…