Related papers: Supersymmetric elements in divided powers algebras
We reconstruct the quantum enveloping superalgebra ${\bf U}(\mathfrak{gl}_{m|n})$ over $\mathbb Q(v)$ via (finite dimensional) quantum Schur superalgebras. In particular, we obtain a new basis containing the standard generators of ${\bf…
We study cohomology for classical Lie superalgebras $\mathfrak{g}$ (e.g. gl(m|n)) over the complex numbers. Using results from invariant theory, we show that there exist subsuperalgebras which detect the cohomology of $\mathfrak{g}.$…
To a finite type knot invariant, a weight system can be associated, which is a function on chord diagrams satisfying so-called $4$-term relations. In the opposite direction, each weight system determines a finite type knot invariant. In…
We show a correspondence between tensor representations of the super general linear group GL(m|n) and tensor representations of the general linear superalgebra gl(m|n) constructed by Berele and Regev.
The Drinfeld-Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalgebras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under…
We introduce the general polynomial algebras characterizing a class of higher order superintegrable systems that separate in Cartesian coordinates. The construction relies on underlying polynomial Heisenberg algebras and their defining…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the…
An inclusion of II$_1$ factors $N \subset M$ with finite Jones index gives rise to a powerful set of invariants that can be approached successfully in a number of different ways. We describe Jones' pictorial description of the standard…
The composition factors of Kac-modules for the general linear Lie superalgebras $gl_{m|n}$ are explicitly determined. In particular, a conjecture of Hughes, King and van der Jeugt in [J. Math. Phys., 41 (2000), 5064-5087] is proved.
$N=1$ supersymmetric gauge theories with global flavor symmetries contain a gauge invariant W-superalgebra which acts on its moduli space of gauge invariants. With adjoint matter, this superalgebra reduces to a graded Lie algebra. When the…
By using certain quantum differential operators, we construct a super representation for the quantum queer supergroup U_v(q_n). The underlying space of this representation is a deformed polynomial superalgebra in 2n^2 variables whose…
The representation theory of symmetric Lie superalgebras and corresponding spherical functions are studied in relation with the theory of the deformed quantum Calogero-Moser systems. In the special case of symmetric pair g=gl(n,2m),…
Adem and Reichstein introduced the ideal of truncated symmetric polynomials to present the permutation invariant subring in the cohomology of a finite product of projective spaces. Building upon their work, I describe a generating set of…
Let R be a commutative ring and let n,m be two positive integers. The symmetric group on n letters acts diagonally on the ring of polynomials in nxm variables with coefficients in R. The subrings of invariants for this action is called the…
In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary…
We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric…
The purpose of this paper is to investigate central elements in distribution algebras $Dist(G)$ of general linear supergroups $G=GL(m|n)$. As an application, we compute explicitly the center of $Dist(GL(1|1))$ and its image under…
In this paper we consider the mixed tensor space of a $\mathbb Z_2$-graded vector space. We obtain a spanning set of invariants of the associated symmetric algebra under the action of the general linear supergroup as well as the queer…
The paper is devoted to invariant theory problems. In particular, to the problem of finding generators of invariant fields in an explicit form. The set of generators is given for invariant field of unitriangular group of adjoint…