相关论文: Super-extensions of tensor algebras and their appl…

This article presents a natural extension of the tensor algebra. In addition to "left multiplications" by vectors, we can consider "derivations" by covectors as basic operators on this extended algebra. These two types of operators satisfy…

This article introduces the duplex Hecke algebra, which is an infinite dimensional algebra generated by two Hecke algebras. This concept originates from the degenerate duplex Hecke algebra in the theory of Schur-Weyl duality related to…

This paper presents a $q$-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori-Hecke algebra type $A$ of infinite degree. Namely this…

The Schur-Weyl duality, which started as the study of the commuting actions of the symmetric group $S_d$ and $\mathrm{GL}(n,\mathbb{C})$ on $V^{\otimes d}$ where $V=\mathbb{C}^n$, was extended by Drinfeld and Jimbo to the context of the…

The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…

In this note, we investigate a kind of double centralizer property for general linear supergroups. For the super space $V=\mathbb{K}^{m\mid n}$ over an algebraically closed field $\mathbb{K}$ whose characteristic is not equal to $2$, we…

Turner's Conjecture describes all blocks of symmetric groups and Hecke algebras up to derived equivalence in terms of certain double algebras. With a view towards a proof of this conjecture, we develop a general theory of Turner doubles. In…

An enhanced algebraic group $\uG$ of $G=\GL(V)$ over $\bbc$ is a product variety $\GL(V)\times V$, endowed with an enhanced cross product. Associated with a natural tensor representation of $\uG$, there are naturally Levi and parabolic…

Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of…

As an analogy of superalgebra of multivector fields with the Schounte bracket, we introduce a non-trivial superbracket on differential forms of manifold. We show properties of this new superalgebra. We extend this superalgebra by adding one…

Two super-analogs of the Schur-Weyl duality are considered: the duality of actions in $(\mathbb{C}^{m|n})^{\otimes N}$ of the Lie superalgebra $\mathfrak{gl}(m,n)$ and the symmetric group $S_N$, and the duality of actions of the Lie…

Let $U_q(\mathfrak{g})$ be the quantized superalgebra of $\mathfrak{g}=\mathfrak{gl}(k_1|\ell_1)\oplus\cdots\oplus\mathfrak{gl}(k_m|\ell_m)$ and $H_{m,n}(q,\mathbf{Q})$ the cyclotomic Hecke algebra of type $G(m,1,n)$. We define a right…

We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of…

After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.

In this paper, we develop the foundations of the representation theory of quiver Hecke--Clifford superalgebras. We further construct a Schur--Weyl duality between quantum affine analogues of the queer Lie superalgebra and the quiver…

We use super $q$-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of $\mathfrak{gl}_N$-modules (and, more generally, $\mathfrak{gl}_{N|M}$-modules) whose objects are tensor…

We construct a class of extended operators in the cohomology of a pair of twisted Schur supercharges of 4d N=2 SCFTs. The extended operators are constructed from the local operators in this cohomology -- the Schur operators -- by a version…

Schur-Weyl duality concerns the actions of $\text{GL}_{n}(\mathbb{C})$ and $S_{k}$ on tensor powers of the form $V^{\otimes k}$ for an $n$-dimensional vector space $V$. There are rich histories within representation theory, combinatorics,…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

We construct Exceptional Field Theory for the group $SO(5,5)$ based on the extended (6+16)-dimensional spacetime, which after reduction gives the maximal $D=6$ supergravity. We present both a true action and a duality-invariant…