An order-reversing duality map for conjugacy classes in Lusztig's canonical quotient
By Pramod N. Achar. 2002
61 citations recorded by the source corpus.
AbstractWe define a partial order on the set No,c of pairs (O,C), where O is a nilpotent orbit and C is a conjugacy class in A(O), Lusztig’s canonical quotient of A(O). We then show that there is a unique order-reversing duality map No,c → LNo,c that has certain properties analogous to those of the original Lusztig–Spaltenstein duality map. This generalizes work of E. Sommers.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0f2717499fe251292d6052c03641a9d16e48ac83
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Automorphic Integral Transforms for Classical Groups I: Endoscopy Correspondences (2012, methodology): “ partition, i.e. corresponding to the zero nilpotent orbit in g∨(C). Then the BarbaschVogan duality η g∨,g(p(ψ)) must be the partition corresponding to the regular nilpotent orbit in g(F) ([BV85] and [Ac03]). Following the existence of the Arthur-Langlands transfer ([Ar12] and [Mk12]) and the automo”
- Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories (2012, methodology): “We will see that, when this happens, certain discrete groups C(ρ) 6= C(ρ′) introduced by Sommers and Achar [28, 29, 30] enter in the description of the Hitchin system, and affect the properties of the Coulomb branch.”