Related papers: Towards a q-series for osp(2|2n)

Linear operators preserving the direct sum of polynomial rings P(m)\oplus P(n) are constructed. In the case |m-n|=1 they correspond to atypical representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite dimensional…

We construct quasi-solvable quantum mechanical matrix models by employing two different methods, the one is universal enveloping algebra of Lie superalgebra and the other is N-fold supersymmetry. For the former we examine the q(2) and…

We present three groups of examples of Wigner Quantum Systems related to the Lie superalgebras $osp(1/6n)$, $sl(1/3n)$ and $sl(n/3)$ and discuss shortly their physical features. In the case of $sl(1/3n)$ we indicate that the underlying…

Let V be a finite-dimensional superspace and G a simple (or a ``close'' to simple) matrix Lie superalgebra, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of G-invariant elements of…

We construct Drinfeld realisations for the quantum affine superalgebras associated with the osp(1|2n)^{(1)}, Sl(1|2n)^{(2)} and osp(2|2n)^{(2)} series of affine Lie superalgebras.

Dynkin's classification of maximal subalgebras of simple finite dimensional complex Lie algebras is generalized to linear Lie superalgebras. Namely, the maximal non-simple irreducible subalgebras of $\mathfrak{gl}(p|q), \mathfrak{q}(n),…

We introduce supergroup analogues of 3-manifold invariants $\hat{Z}$, also known as homological blocks, which were previously considered for ordinary compact semisimple Lie groups. We focus on superunitary groups, and work out the case of…

For the orthogonal Lie algebra O(2n+1), in addition to the conventional set of orthogonal polynomials, another set is produced with the help of the Lie superalgebra OSP(1|2n). Difficulties related with expression of Dyson's constant for the…

We introduce a modified quantum enveloping algebra as well as a (modified) covering quantum algebra for the ortho-symplectic Lie superalgebra osp(1|2). Then we formulate and compute the corresponding canonical bases, and relate them to the…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

We examine two different m-traces in the category of representations over the quantum Lie superalgebra associated to $\mathfrak{sl}(m|n)$ at root of unity. The first m-trace is on the ideal of projective modules and leads to new Extended…

The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple…

In this paper, we study the existence and classification problems of left-symmetric superalgebras on special linear Lie superalgebras ${\mathfrak{sl}}(m|n)$ with $m\neq n$. The main three results of this paper are: (i) a complete…

The co-Lie structures compatible with the osp(2|2) Lie super algebra structure are investigated and found to be all of coboundary type. The corresponding classical r-matrices are classified into several disjoint families. The osp(1|2)+u(1)…

Three-manifold invariants $\hat Z$ (''$Z$-hat''), also known as homological blocks, are $q$-series with integer coefficients. Explicit $q$-series form for $\hat Z$ is known for $SU(2)$ group, supergroup $SU(2|1)$ and ortho-symplectic…

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order…

In this article we construct link invariants and 3-manifold invariants from the quantum group associated with Lie superalgebra $\mathfrak{sl}(2|1)$. This construction based on nilpotent irreducible finite dimensional representations of…

We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity,…

In this paper, we establish a converse to Schur's theorem for Lie superalgebras \( L \), focusing on cases where the minimal generator number pairs \((p \vert q)\) of \( L/Z(L) \) are considered, and where the superdimension \(…

We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the…