Representations of shifted Yangians and finite W-algebras

Abstract

We study highest weight representations of shifted Yangians over an algebraically closed field of characteristic 0. In particular, we classify the finite dimensional irreducible representations and explain how to compute their Gelfand-Tsetlin characters in terms of known characters of standard modules and certain Kazhdan-Lusztig polynomials. Our approach exploits the relationship between shifted Yangians and the finite W-algebras associated to nilpotent orbits in general linear Lie algebras.

109 pages; v3: substantial changes to treatment of Whittaker functor in chapter 8, minor related changes elsewhere including modified definition of the finite W-algebra

References in corpus (2)

• Crystal structures arising from representations of $GL(m|n)$
• Representation Theory of W-Algebras

Cited by in corpus (23)

• Graded decomposition numbers for cyclotomic Hecke algebras
• Yangians and quantizations of slices in the affine Grassmannian
• Principal W-algebras for GL(m|n)
• Quantized Coulomb branches of Jordan quiver gauge theories and cyclotomic rational Cherednik algebras
• On the structure of the category O for W-algebras
• The degenerate analogue of Ariki's categorification theorem
• Representation theory of W-algebras, II: Ramond twisted representations
• Rationality and Fusion Rules of Exceptional W-Algebras
• Finite W-superalgebras via super Yangians
• A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• Yangian characters and classical W-algebras
• Gelfand-Tsetlin bases for representations of finite W-algebras and shifted Yangians
• Dimensions of irreducible modules over W-algebras and Goldie ranks
• Categorification of tensor product representations of sl(k) and category O
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Gelfand-Kirillov Conjecture and Harish-Chandra Modules for Finite W-Algebras
• Universal filtered quantizations of nilpotent Slodowy slices
• On category $\mathcal{O}$ for affine Grassmannian slices and categorified tensor products
• Rational representations of the Yangian Y(gl_n)
• Irreducible Specht modules for Iwahori-Hecke algebras of type B
• Super Vust theorem and Schur-Sergeev duality for principal finite $W$-superalgebras
• Quantum Sugawara operators in type $A$