Z/m-graded Lie algebras and perverse sheaves, I

We give a block decomposition of the equivariant derived category arising from a cyclically graded Lie algebra. This generalizes certain aspects of the generalized Springer correspondence to the graded setting.

[1]  G. Lusztig,et al.  ℤ/𝕞ℤ-graded Lie algebras and perverse sheaves, III: Graded double affine Hecke algebra , 2016, Representation Theory of the American Mathematical Society.

[2]  L. Rider,et al.  Perverse Sheaves on the Nilpotent Cone and Lusztig's Generalized Springer Correspondence , 2014, 1409.7132.

[3]  G. Lusztig.  Study of antiorbital complexes , 2009, 0910.4147.

[4]  G. Lusztig.  Graded Lie Algebras and Intersection Cohomology , 2006, math/0604535.

[5]  D. Alvis.  Induce/restrict matrices for exceptional Weyl groups , 2005, math/0506377.

[6]  E. Vasserot.  Induced and simple modules of double affine Hecke algebras , 2002, math/0207127.

[7]  G. Lusztig.  Cuspidal local systems and graded Hecke algebras, III , 2001, math/0108173.

[8]  G. Lusztig.  Study of Perverse Sheaves Arising from Graded Lie Algebras , 1995 .

[9]  George Lusztig,et al.  Canonical bases arising from quantized enveloping algebras , 1990 .

[10]  D. Kazhdan,et al.  Proof of the Deligne-Langlands conjecture for Hecke algebras , 1987 .

[11]  George Lusztig,et al.  Character sheaves, V , 1985 .

[12]  G. Lusztig.  Intersection cohomology complexes on a reductive group , 1984 .

[13]  W. M. Beynon,et al.  Green functions of finite Chevalley groups of type En (n = 6, 7, 8) , 1984 .

[14]  George Lusztig,et al.  Characters of reductive groups over a finite field , 1984 .

[15]  T. Shoji.  On the Green polynomials of classical groups , 1983 .

[16]  G. Lusztig.  Green polynomials and singularities of unipotent classes , 1981 .

[17]  D. Kazhdan,et al.  Representations of Coxeter groups and Hecke algebras , 1979 .

[18]  T. A. Springer.  A construction of representations of Weyl groups , 1978 .

[19]  T. A. Springer.  Trigonometric sums, green functions of finite groups and representations of Weyl groups , 1976 .

[20]  G. Lusztig.  On the Green Polynomials of Classical Groups , 1976 .

[21]  È. Vinberg,et al.  THE WEYL GROUP OF A GRADED LIE ALGEBRA , 1976 .

[22]  B. Kostant,et al.  On orbits associated with symmetric spaces , 1969 .

[23]  B. Kostant,et al.  The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group , 1959 .

[24]  George Luztig.  Character Sheaves I , 2003 .

[25]  T. Shoji.  On the springer representations of the weyl groups of classical algebraic groups , 1979 .

[26]  G. Lusztig.  Representations Of Finite Chevalley Groups , 1978 .

[27]  Robert Steinberg,et al.  Endomorphisms of linear algebraic groups , 1968 .

[28]  E. B. Dynkin,et al.  Semisimple subalgebras of semisimple Lie algebras , 1957 .

[29]  N. Jacobson.  Completely Reducible Lie Algebras of Linear Transformations , 1951 .