Notes on Affine Hecke Algebras I.
(Degenerated Hecke Algebras and Yangians in Mathematical Physics)

Arun Ram
Department of Mathematics and Statistics
University of Melbourne
Parkville, VIC 3010 Australia
aram@unimelb.edu.au

Last update: 23 April 2014

Notes and References

This is an excerpt of the paper Notes on Affine Hecke Algebras I. (Degenerated Hecke Algebras and Yangians in Mathematical Physics) by Ivan Cherednik.

Bibliography

[Zam1978] A.B. Zamolodchikov, Relativistic factorized S-matrix in two dimensions having O(N) isotopic symmetry, Nuclear Physics B133 (1978) 525.

[Che1979] I.V. Cherednik, On some S-matrices, connected with abelian varieties, Doklady AN SSSR, 249, No. 5 (1979) 1095.

[Che1984] I.V. Cherednik, Factorized particles on a half-line and root systems, Theor. Math. Phys. 61 No. 1 (1984) 35.

[KZa1984] V.G. Knizhnik and A.B. Zamolodchikov, Current algebra and Wess-Zumino models in two dimensions, Nucl. Physics B247 (1984) 83.

[Che1991] I. Cherednik, Monodromy representations for generalized Knizhnik-Zamolodchikov equations and Hecke algebras, Publ. RIMS, Kyoto Univ. 27 (1991), 711–726.

[Dri1986] V.G. Drinfeld, Degenerate affine Hecke algebras and Yangians, Funct. Anal. Appl. 20 (1986), 58-60.

[Che1987] I.V. Cherednik, A new interpretation of Gel’fand-Tzetlin bases, Duke Math. J. 54 (1987), 563–577.

[Rog1985] J.D. Rogawski, On modules over the Hecke algebra of a p-adic group, Invent. Math. 79 (1985) 443–465. MR 86j:22028

[Che1986-2] I.V. Cherednik, On special bases of irreducible representations of the degenerated affine Hecke algebra, Funktsion. Anal. Prilozhen., 20, No. 1, 87-88 (1986).

[FRS1989] K. Fredenhagen, K.H. Rehren and B. Schroer, Superselection sectors with braid group statistics and exchange algebras, Commun. Math. Phys. 125 (1989) 201.

[MSc1990] G. Mack and V. Schomerus, Conformal field algebra with quantum symmetry from the theory of superselection sectors, Preprint (1990).

[Che1989] I.V. Cherednik, Quantum groups as hidden symmetries of classic representation theory, Proceed. of 17th Int. Conference on differential geometric methods in theoretical physics, (Chester, 1988), World Scient. (1989) 47.

[Fad1984] L.D. Faddeev, Integrable models in (1+1)-dimensional quantum field theory, (Lectures in Les Houches, 1982), Elsevier Science Publishers B:V., 1984.

[Dri1987] V.G. Drinfeld, Quantum Groups, Vol. 1 of Proceedings of the International Congress of Mathematicians, Berkley, California USA, 1986, Academic Press, 1987, pp. 798-820.

[Che1986] I.V. Cherednik, On R-matrix quantization of formal loop groups. Group theoretic methods in physics, Proceedings of the 3rd Int. Sem. [in Russian], Nauka, Moscow 1986 (VNU Publ. B.V., 1986).

[Dri1989-2] V.G. Drinfeld, Quasi-Hopf algebras and Knizhnik-Zamolodchikov equations, Problems of modern quantum field theory (Alushta, 1989), 1–13, Res. Rep. Phys., Springer 1989

[MSe1989] G. Moore and N. Seiber, Classical and quantum conformal field theory, Comm. Math. Phys. Volume 123, Number 2 (1989), 177-254.

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