Lusztig's Canonical Quotient and Generalized Duality

Lusztig’s Canonical Quotient and Generalized Duality

We give a new characterization of Lusztig’s canonical quotient, a finite group attached to each special nilpotent orbit of a complex semisimple Lie algebra. This group plays an important role in the classification of unipotent representations of finite groups of Lie type. We also define a duality map. To each pair of a nilpotent orbit and a conjugacy class in its fundamental group, the map assi...

Duality and Canonical Transformations

We present a brief review on the canonical transformation description of some duality symmetries in string and gauge theories. In particular, we consider abelian and non-abelian T-dualities in closed and open string theories as well as S-duality in abelian and non-abelian non-supersymmetric gauge theories. THU-96/36 hep-th/9610024 October 1996 Talk given at the Argonne Duality Institute, June 2...

An Order-reversing Duality Map for Conjugacy Classes in Lusztig’s Canonical Quotient

We define a partial order on the set No,c̄ of pairs (O, C), where O is a nilpotent orbit and C is a conjugacy class in Ā(O), Lusztig’s canonical quotient of A(O). We then show that there is a unique order-reversing duality map No,c̄ → LNo,c̄ that has certain properties analogous to those of the original Lusztig-Spaltenstein duality map. This generalizes work of E. Sommers.

Generalized Quotient Rings

FUZZY SEMI-IDEAL AND GENERALIZED FUZZY QUOTIENT RING

The concepts of fuzzy semi-ideals of R with respect to H≤R and generalized fuzzy quotient rings are introduced. Some properties of fuzzy semiideals are discussed. Finally, several isomorphism theorems for generalized fuzzy quotient rings are established.