Suppose that the underlying field is of characteristic different from 2 and 3. We first prove so-called stem deformations a free presentation finite-dimensional Lie superalgebra L exhaust all maximal extensions L, up to equivalence extensions. Then we multipliers covers always exist for they are unique isomorphisms. Finally, describe multipliers, covers, Heisenberg superalgebras model filiform ...

The odd reflections are an effective tool in the Lie superalgebra representation theory, as they relate non-conjugate Borel subalgebras. We introduce analogues of for Yangian \( \mathrm{Y}(\mathfrak {gl}_{m|n})\) and use them to produce a transition rule parameters highest weight modules corresponding change parity sequence. This leads description finite-dimensional irreducible representations ...

In this paper, we study the representations of periplectic Lie superalgebra using Duflo-Serganova functor. Given a simple $\mathfrak{p}(n)$-module $L$ and certain element $x\in \mathfrak{p}(n)$ rank $1$, give an explicit description composition factors $\mathfrak{p}(n-1)$-module $DS_x(L)$, which is defined as homology complex $$\Pi M \xrightarrow{x} \Pi M.$$ particular, show that multiplicity-f...

We propose to parametrize the configuration space of one-dimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the Hamiltonians of the AN , BCN , BN , CN and DN Calogero and Sutherland models, as well as their supersymmetric generalizations, can be expressed — for arbitrary valu...

The type-I simple Lie-superalgebras are sl(m|n) and osp(2|2n). We study the quantum deformations of their untwisted affine extensions Uq(sl(m|n) (1)) and Uq(osp(2|2n) (1)). We identify additional relations between the simple generators (“extra q-Serre relations”) which need to be imposed to properly defineUq(sl(m|n) (1)) and Uq(osp(2|2n) (1)). We present a general technique for deriving the spe...

We obtain a closed form expression of the universal T-matrix encapsulating the duality of the quantum superalgebra U q [osp(1/2)] and the corresponding supergroup OSp q (1/2). The classical q → 1 limit of this universal T matrix yields the group element of the undeformed OSp(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp q (1/2) are readily constructed emp...

We obtain a closed form expression of the universal T-matrix encapsulating the duality between the quantum superalgebra U q [osp(1/2)] and the corresponding su-pergroup OSp q (1/2). The classical q → 1 limit of this universal T matrix yields the group element of the undeformed OSp(1/2) supergroup. The finite dimensional representations of the quantum supergroup OSp q (1/2) are readily construct...

An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V (p), with a lowest weight of the form [−p2 , . . . ,− p 2 | p 2 , . . . , p 2 ], p being a positive integer. Explicit expressions for the transformation of the basis unde...