Abstract
Methods are developed for systematically constructing the finite-dimensional irreducible representations of the super Yangian Y (gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite-dimensional irreducible representation of Y (gl(M|N)) is of highest weight type, and is uniquely characterized by a highest weight. The necessary and sufficient conditions for an irrep to be finite-dimensional are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Zhang, R. B.: J. Math. Phys. 36 (1995), 3854.
Drinfeld, V. G.: Soviet Math. Dokl. 36 (1988), 212.
Tarasov, V. O.: Theor. Math. Phys. 61 (1984), 163; 63 (1985), 175.
Cherednik, I. V.: Duke Math. J. 54 (1987), 563.
Chari, V. and Pressley, A.: J. Reine Angew. Math. 417 (1991), 87.
Kirillov, A. N. and Reshetikhin, N. Yu.: Lett. Math. Phys. 12 (1986), 199.
Reshetikhin, N. Yu.: Theor. Math. Phys. 63 (1985), 347.
Molev, A.: Lett. Math. Phys. 30 (1994), 53.
Nazarov, M. L.: Lett. Math. Phys. 21 (1991), 123.
Zhang, R. B.: Lett. Math. Phys. 33 (1995), 263.
Kac, V. G.: Adv. Math. 26 (1977), 8; Scheunert, M.: Lecture Notes in Math. 716, Springer-Verlag, Berlin, 1979.
Gerstenhaber, M.: Ann. Math. 78 (1963), 267.
Zhang, R. B.: J. Math. Phys. 34 (1993), 1236; J. Phys. A 26 (1993), 7041.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhang, R.B. The gl (M|N) super Yangian and its finite-dimensional representations. Lett Math Phys 37, 419–434 (1996). https://doi.org/10.1007/BF00312673
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00312673