Quasifinite Representations of Classical Subalgebras of the Lie Superalgebra of Quantum Pseudodifferential Operators
Quasifinite Representations of Classical Subalgebras of the Lie Superalgebra of Quantum Pseudodifferential Operators
We classify the anti-involutions of the superalgebra of quantum pseudodifferential operators on the super circle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mi>S</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mrow></mml:msup></mml:mrow></mml:math> preserving the principal gradation, producing in this way a family of Lie subalgebras minus fixed by these anti-involutions. We classify the irreducible quasifinite highest weight representations of the central extension of …