TRANSVERSE POISSON STRUCTURES TO ADJOINT ORBITS IN A COMPLEX SEMI-SIMPLE LIE ALGEBRA

Explore the concept of transverse Poisson structures in relation to adjoint orbits within complex semi-simple Lie algebras in this conference talk from GSI. Delve into Arthur Weinstein's splitting theorem and its implications for Poisson manifolds. Examine the structure of symplectic leaves and transverse slices in the context of coadjoint orbits. Investigate the conditions under which transverse Poisson structures become polynomial, with a focus on semi-simple Lie algebras. Analyze the reduction of general adjoint orbits to nilpotent orbits and the resulting quasihomogeneous polynomial expressions. Discover the determinantal formula for subregular nilpotent orbits and its connection to the singular variety of nilpotent elements in the slice.