On Modules over Matrix Quantum Pseudo-Differential Operators.

C. BOYALLIAN Y J. LIBERATI

LETTERS IN MATHEMATICAL PHYSICS

SPRINGER

Año: 2002 vol. 60 p. 73 - 85

0377-9017

We classify all the quasifinite highest weight modules over the central extension of the Lie algebra of matrix quantum pseudo-differential operators, and obtain them in terms of representation theory of the Lie algebra ${\widehat g}l(\infty , R_m)$ of infinite matrices with only finitely many non-zero diagonals over the algebra $R_m={\Bbb C}[t]/(t^{m+1})$. We also classify the unitary ones.