We explicitly construct the Lax pair (L,A) for the N-extended supersymmetric Calogero--Moser models.
Having obtained such a representation, which correctly reproduces all equations of motion, we consider the integrability of these models.
To represent the structure of conserved currents, we derive the complete set of Liouville charges,
which depend on lower powers of momentum, for the...
Quantum spin chains and their degenerations, quantum Gaudin models, play an important role in modern mathematics. The study of these integrable models is interlaced with such areas as the representation theory of Lie algebras and their deformations, the quantum cohomology and K-theory of quiver varieties, the geometric Langlands correspondence.
It is natural to study Lie-theoretic...
We revisit the construction of supersymmetric Schwarzians using nonlinear realizations. We show that supersymmetric Schwarzians can be systematically
obtained as certain projections of Maurer-Cartan forms of superconformal groups after imposing simple conditions on them.
We also present the supersymmetric Schwarzian actions, defined as the integrals of products of Cartan forms. In contrast...
First, we consider the relationship between super Yangians and quantum loop superalgebras. We consider structures of tensor categories on analogs of the category $\mathfrak{O}$ for representations of the super Yangian $Y_{\hbar}(A(m,n))$ of the special linear Lie superalgebra and the quantum loop superalgebra $U_q(LA(m,n)) $, explore the relationship between them. The construction of an...
Shapovalov elements $\theta_{\beta,m}$ in the classical or quantum universal enveloping algebra of the negative Borel subalgebra of a simple Lie algebra are parameterized by a positive root $\beta$ and a positive integer $m$. They relate the canonical generator of a reducible Verma module with highest vectors of its Verma submodules. We obtain a factorization of $\theta_{\beta,m}$ to a...
