Classification of finite irreducible modules over the Lie conformal superalgebra CK6

We classify all continuous degenerate irreducible modules over the exceptional linearly compact Lie superalgebra E(1, 6), and all finite degenerate irreducible modules over the exceptional Lie conformal superalgebra CK6, for which E(1, 6) is the annihilation algebra

Graded associative conformal algebras of finite type

In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\Gamma$ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\simeq \Gamma$. A classification of simple and semisimple graded associative conformal algebras of finite type is obtained

Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

Pairs of $n\times n$ matrices whose commutator differ from the identity by a matrix of rank $r$ are used to construct bispectral differential operators with $r\times r$ matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case $r=1$, this reproduces well-known results of Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators. This new class of pairs $(L, \Lambda)$ of bispectral matrix differential operators is different than those previously studied in that $L$ acts from the left, but $\Lambda$ from the right on a common $r\times r$ eigenmatrix.Comment: 16 page