Parabolic Presentations of the Yangian
By Jonathan Brundan, Alexander S. Kleshchev. 2004
79 citations recorded by the source corpus.
We introduce some new presentations for the Yangian associated to the Lie algebra These presentations are parametrized by tuples of positive integers summing to n. At one extreme, for the tuple (n), the presentation is the usual RTT presentation of Yn. At the other extreme, for the tuple (1n), the presentation is closely related to Drinfeld’s presentation. In general, the presentations are useful for understanding the structure of the standard parabolic subalgebras of Yn.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/d2e5d70c3be3fd79a04467ecdf41fd4aa073d031
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
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Citations in the corpus
- On the R-Matrix Realization of Yangians and their Representations (2005, background): “(A detailed construction of such an isomorphism in the case of Y(slN) is recently given by Brundan and Kleshchev [ 5 ].) Therefore, the classification results of [12] do not imply an immediate description of the finite-dimensional irreducible representations of the extended Yangian X(a).”