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math.SG2026
Generalized Gelfand-Cetlin data and abelianization
Peter Crooks, Mitchell Pound
This manuscript aims to advance existing approaches to the abelianization of symplectic quotients. Two such approaches include the imploded cross-sections of Guillemin-Jeffrey-Sjam…
math.RT2026
Poisson blow-ups and the adjoint quotient
Peter Crooks, Iva Halacheva
We leverage Polishchuk's Poisson blow-up criterion in the context of algebro-geometric integrable systems. In more detail, one may associate an integrable system $τ:\mathfrak{X}\lo…