Extremal Projector and Dynamical Twist
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 158-176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We describe a relation between the dynamical twist $J(\lambda)$ and the extremal projector for simple Lie algebras. This correspondence finds two obvious applications: first, the solution of the Arnaudon–Buffenoir–Ragoucy–Roche equation can be obtained from the known multiplicative expression for the extremal projector; second, the structure constants are determined by the matrix coefficients of the dynamical twist.
Keywords: extremal projector, dynamical twist.
@article{TMF_2004_139_1_a11,
     author = {S. M. Khoroshkin},
     title = {Extremal {Projector} and {Dynamical} {Twist}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {158--176},
     year = {2004},
     volume = {139},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a11/}
}
TY  - JOUR
AU  - S. M. Khoroshkin
TI  - Extremal Projector and Dynamical Twist
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2004
SP  - 158
EP  - 176
VL  - 139
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a11/
LA  - ru
ID  - TMF_2004_139_1_a11
ER  - 
%0 Journal Article
%A S. M. Khoroshkin
%T Extremal Projector and Dynamical Twist
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2004
%P 158-176
%V 139
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a11/
%G ru
%F TMF_2004_139_1_a11
S. M. Khoroshkin. Extremal Projector and Dynamical Twist. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 158-176. http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a11/

[1] J. Mickelsson, Rep. Math. Phys., 4:4 (1973), 303–318 | DOI | MR

[2] R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoi, Matem. zametki, 26 (1979), 15–25 | MR | Zbl

[3] D. P. Zhelobenko, Izv. AN SSSR. Ser. matem., 52:4 (1988), 758–773

[4] D. P. Zhelobenko, Predstavleniya reduktivnykh algebr Li, Nauka, M., 1994 | MR | Zbl

[5] G. Felder, “Conformal field theory and integrable systems associated with elliptic curves”, Proc. of the Intern. Congress of Mathematicians (Zurich, Aug. 3–11, 1994), Birkhaüser, Basel, 1995, 1247–1255 | DOI | MR | Zbl

[6] D. Arnaudon, E. Buffenoir, E. Ragoucy, Ph. Roche, Lett. Math. Phys., 44:3 (1998), 201–214 | DOI | MR | Zbl

[7] P. Etingof, O. Schiffmann, “Lectures on the dynamical Yang–Baxter equation”, Quantum groups and Lie theory (Durham 1999), London Math. Soc. Lect. Notes Ser., 290, ed. A. Pressley, Cambridge Univ. Press, Cambridge, 2001 ; E-print math.QA/9908064 | MR | Zbl

[8] P. Etingof, A. Varchenko, Commun. Math. Phys., 205:1 (1999), 19–52 | DOI | MR | Zbl

[9] V. N. Tolstoi, UMN, 44:1 (1989), 211–212 | MR

[10] S. M. Khoroshkin, V. N. Tolstoy, “Extremal projector and universal $R$-matrix for quantized contragredient Lie (super)algebras”, Quantum Groups and Related Topics, Proc. of the First Max Born Symp. (Wroclaw, 1991), Math. Phys. Stud., 13, ed. R. Gielerak, Kluwer, Dordrecht, 1992, 23–32 | MR | Zbl

[11] A. Joseph, G. Letzter, J. Algebra, 153 (1992), 289–318 | DOI | MR | Zbl

[12] V. G. Drinfeld, Algebra i analiz, 1:2 (1989), 30–46 | MR

[13] P. Etingof, A. Varchenko, Adv. Math., 167:1 (2002), 74–127 ; V. Tarasov, A. Varchenko, Int. Math. Res. Notices, 15 (2000), 801–829 | DOI | MR | Zbl | DOI | MR | Zbl