The Spin Calogero-Sutherland Model at Infinity

Abstract

For N = 1, 2, . . . we consider an action of the Yangian Y(gl n ) on N th symmetric power of the space of polynomials in one variable with coefficients in C n . This action is given by the Heckman operators [9] via the Drinfeld functor [6]. We describe the limit of this action at N → ∞ . This provides another solution to the problem already considered in [11].

Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system

“…These constructions heavily use an equivariant family of Heckman-Dunkl [6] operators as a counterpart of the Lax operator in integrable systems. The procedure requires a creation of an auxiliary space of functions symmetric over all variables except one [15,16] or as a variant of polynomials in one variable with coefficients being symmetric functions of all variables [14,18]. These spaces are created by the vertex operator…”

“…This limiting bosonic construction system was generalized in [9] to spin CS system using the language of polysymmetric functions, that is polynomials, symmetric on the groups of variables. See also [14].…”

Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system

“…These constructions heavily use an equivariant family of Heckman-Dunkl [6] operators as a counterpart of the Lax operator in integrable systems. The procedure requires a creation of an auxiliary space of functions symmetric over all variables except one [15,16] or as a variant of polynomials in one variable with coefficients being symmetric functions of all variables [18,14]. These spaces are created by the vertex operator…”