15 research outputs found
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 is a
pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group
such that the identity component is the affine line and . 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 matrices whose commutator differ from the identity by a
matrix of rank are used to construct bispectral differential operators with
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 , 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
of bispectral matrix differential operators is different than
those previously studied in that acts from the left, but from the
right on a common eigenmatrix.Comment: 16 page