54 research outputs found
Finite-dimensional irreducible representations of twisted Yangians
We study quantized enveloping algebras called twisted Yangians. They are
analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D
series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with
respect to the coproduct in Y(gl(N)). We give a complete description of their
finite-dimensional irreducible representations. Every such representation is
highest weight and we give necessary and sufficient conditions for an
irreducible highest weight representation to be finite-dimensional. The result
is analogous to Drinfeld's theorem for the ordinary Yangians. Its detailed
proof for the A series is also reproduced. For the simplest twisted Yangians we
construct an explicit realization for each finite-dimensional irreducible
representation in tensor products of representations of the corresponding Lie
algebras.Comment: AMSTEX, 59 page
A Basis for Representations of Symplectic Lie Algebras
A basis for each finite-dimensional irreducible representation of the
symplectic Lie algebra sp(2n) is constructed. The basis vectors are expressed
in terms of the Mickelsson lowering operators. Explicit formulas for the matrix
elements of generators of sp(2n) in this basis are given. The basis is natural
from the viewpoint of the representation theory of the Yangians. The key role
in the construction is played by the fact that the subspace of sp(2n-2)-highest
vectors in any finite-dimensional irreducible representation of sp(2n) admits a
natural structure of a representation of the Yangian Y(gl(2)).Comment: 34 pages, AmSTe
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