pith:ABHBHCWB
Quasi-Poisson Modules and Harish-Chandra $\bs{AD}$-Modules
Simple cuspidal quasi-Poisson modules over a Lie-Rinehart pair correspond one-to-one with simple cuspidal Harish-Chandra modules.
arxiv:2605.16950 v1 · 2026-05-16 · math.RT
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Claims
there is a one-to-one correspondence between simple cuspidal quasi-Poisson modules over (dot A, dot fk) and simple cuspidal Harish-Chandra A fk-modules for A:= C[t0^{pm1}] ot dot A and fk:= Der(A). We also classify simple cuspidal quasi-Poisson modules over the Lie-Rinehart pair (dot A, dot fk) and show that each such module is a tensor module dot A ot Omega for an admissible gl(m+1,n)-module Omega via a prescribed action.
The specific algebraic setup with dot A = C[t1^{pm1},...,tm^{pm1}] ot Lambda_n and the restriction to cuspidal simple modules; the correspondence and classification are stated only for this choice of Lie-Rinehart pair and module class, so the result depends on these structural choices holding exactly as defined.
Defines quasi-Poisson modules over Lie-Rinehart pairs and establishes a bijection with Harish-Chandra modules, classifying simple cuspidal examples as tensor modules over gl(m+1,n).
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Receipt and verification
| First computed | 2026-05-20T00:03:32.484307Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
004e138ac1d41aa239a61765a5d94398c06400a855246fef7a1f1f735d37e0de
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Canonical record JSON
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