Abstract
We study the equivalence classes of the non-resonant subquotients of spaces of pseudodifferential operators between tensor density modules over the superline \(\mathbb {R}^{1|1}\), as modules of the Lie superalgebra of contact vector fields. There is a 2-parameter family of subquotients with any given Jordan-Hölder composition series. We give a complete set of even equivalence invariants for subquotients of all lengths l. In the critical case l = 6, the even equivalence classes within each non-resonant 2-parameter family are specified by a pencil of conics. In lengths l ≥ 7 our invariants are not fully simplified: for l = 7 we expect that there are only finitely many equivalences other than conjugation, and for l ≥ 8 we expect that conjugation is the only equivalence. We prove this in lengths l ≥ 15. We also analyze certain lacunary subquotients.
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Communicated by: Vyjayanthi Chari
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Conley, C.H. Equivalence Classes of Subquotients of Supersymmetric Pseudodifferential Operator Modules. Algebr Represent Theor 18, 665–692 (2015). https://doi.org/10.1007/s10468-014-9511-x
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DOI: https://doi.org/10.1007/s10468-014-9511-x