Q-W-algebras, Zhelobenko operators and a proof of De Concini-Kac-Procesi conjecture
arXiv:2102.03208
Abstract
This monograph, along with a self-consistent presentation of the theory of q-W-algebras including the construction of algebraic group analogues of Slodowy slices, contains a description of q-W-algebras in terms of Zhelobenko type operators introduced in the book. This description is applied to prove the De Concini-Kac-Procesi conjecture on the dimensions of irreducible modules over quantum groups at roots of unity.
248 pages, deeply revised version; the proof of the cross-section theorem for algebraic group analogues of Slodowy slices is significantly simplified; the construction of Zhelobenko type operators for q-W-algebras in Chapter 4 is revised using some new results on the adjoint action of the quantum group in Chapter 2; more details in some proofs in Chapter 4 are presented