SIGMA 10 (2014), 098, 7 pages arXiv:1403.6817
Contribution to the Special Issue on New Directions in Lie Theory
Center of Twisted Graded Hecke Algebras for Homocyclic Groups
Wee Liang Gan a and Matthew Highfield b
a) University of California, Riverside, CA 92521, USA
b) Pepperdine University, Malibu, CA 90263, USA
Received March 31, 2014, in final form October 10, 2014; Published online October 15, 2014
We determine explicitly the center of the twisted graded Hecke algebras associated to homocyclic groups. Our results are a generalization of formulas by M. Douglas and B. Fiol in [J. High Energy Phys. 2005 (2005), no. 9, 053, 22 pages].
twisted graded Hecke algebra; homocyclic group.
pdf (330 kb)
tex (11 kb)
Căldăraru A., Giaquinto A., Witherspoon S., Algebraic deformations arising from orbifolds with discrete torsion, J. Pure Appl. Algebra 187 (2004), 51-70, math.KT/0210027.
Chmutova T., Twisted symplectic reflection algebras, math.RT/0505653.
Douglas M.R., Fiol B., D-branes and discrete torsion. II, J. High Energy Phys. 2005 (2005), no. 9, 053, 22 pages, hep-th/9903031.
Drinfel'd V.G., Degenerate affine Hecke algebras and Yangians, Funct. Anal. Appl. 20 (1986), 58-60.
Lusztig G., Cuspidal local systems and graded Hecke algebras. I, Inst. Hautes Études Sci. Publ. Math. (1988), 145-202.
Lusztig G., Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), 599-635.
Ram A., Shepler A.V., Classification of graded Hecke algebras for complex reflection groups, Comment. Math. Helv. 78 (2003), 308-334, math.GR/0209135.
Walton C.M., On degenerations and deformations of Sklyanin algebras, Ph.D. Thesis, University of Michigan, 2011.
Witherspoon S., Skew derivations and deformations of a family of group crossed products, Comm. Algebra 34 (2006), 4187-4206, math.RA/0506154.
Witherspoon S., Twisted graded Hecke algebras, J. Algebra 317 (2007), 30-42, math.RT/0506152.