Factorizations of relative extremal projectors
Tóm tắt
We survey earlier results on factorizations of extremal projectors and relative extremal projectors and present preliminary results on non-commutative factorizations of relative extremal projectors: we deduce the existence of such factorizations for sl4 and sl5.
Tài liệu tham khảo
R. Asherova, Y. Smirnov and V. Tolstoi, “Description of a class of projection operators for semisimple complex Lie algebras,” Math. Notes 26, 499–504 (1979).
C. H. Conley and M. R. Sepanski, “Relative extremal projectors,” Adv. Math. 174 (2), 155–166 (2003).
C. H. Conley and M. R. Sepanski, “Infinite commutative product formulas for relative extremal projectors,” Adv. Math. 196, 52–77 (2005).
P. Etingof and A. Varchenko, “Dynamical Weyl groups and applications,” Adv. Math. 167 (1), 74–127 (2002).
A. Molev, Yangians and Classical Lie Algebras, Math. Surveys and Monographs 143 (American Math. Society, Providence, 2007).
V. Tarasov and A. Varchenko, “Difference equations compatible with trigonometric KZ differential equations,” Int. Math. Res. Notices 2000 (15), 801–829.
D. P. Zhelobenko, “Extremal cocycles of Weyl groups,” Funct. Anal. Appl. 21 (3), 11–21 (1987).
D. P. Zhelobenko, “S-algebras and Harish-Chandra modules over symmetric Lie algebras,” Izv. Akad. Nauk SSSR Ser. Mat. 54 (4), 659–675 (1990).
D. P. Zhelobenko, “Constructive modules and extremal projectors over Chevalley algebras,” Funct. Anal. Appl. 27 (3), 158–165 (1993).