Shifted Yangians and Finite W -algebras

@inproceedings{Kleshchev2004ShiftedYA,
  title={Shifted Yangians and Finite W -algebras},
  author={Alexander Kleshchev},
  year={2004}
}
We give a presentation for the finite W -algebra associated to a nilpotent matrix inside the general linear Lie algebra over C. In the special case that the nilpotent matrix consists of n Jordan blocks each of the same size l, the presentation is that of the Yangian of level l associated to the Lie algebra gln, as was first observed by Ragoucy and Sorba. In the general case, we are lead to introduce some generalizations of the Yangian which we call the shifted Yangians. 
Highly Cited
This paper has 21 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Special transverse slices and their enveloping algebras

  • A. Premet
  • Advances Math
  • 2002

Ragoucy, RTT presentation of finite W -algebras

  • E. C. Briot
  • J. Phys. A
  • 2001

Quantum groups as hidden symmetries of classic representation theory, in: “Differential geometric methods in theoretical physics (Chester

  • I. Cherednik
  • World Sci. Publishing,
  • 1988

Simple singularities and simple algebraic groups, Lecture

  • P. Slodowy
  • Notes in Math.,
  • 1980

Generalized Whittaker vectors and representation theory

  • T. E. Lynch
  • PhD thesis, M.I.T.,
  • 1979

On Whittaker modules and representation theory

  • B. Kostant
  • Invent. Math
  • 1978

Conjugacy classes”, in: Seminar on algebraic groups and related topics, eds: A

  • T. Springer, R. Steinberg
  • Borel et al., Lecture Notes in Math. 131,
  • 1970

Similar Papers

Loading similar papers…