منابع مشابه
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...
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The Yangian Y (g) associated to a finite-dimensional complex simple Lie algebra g is a Hopf algebra deformation of the universal enveloping algebra of the Lie algebra g[u] of polynomial maps C → g (with Lie bracket defined pointwise). It is important to understand the finite-dimensional representations of Y (g). For one thing, they are closely related to rational solutions of the so-called quan...
متن کاملSkew representations of twisted Yangians
Analogs of the classical Sylvester theorem have been known for matrices with entries in noncommutative algebras including the quantized algebra of functions on GLN and the Yangian for glN . We prove a version of this theorem for the twisted Yangians Y(gN) associated with the orthogonal and symplectic Lie algebras gN = oN or spN . This gives rise to representations of the twisted Yangian Y(gN−M ...
متن کاملUnderstanding Irreducible Representations
This paper acts as an introduction to representation theory. In addition to defining representations of Lie algebras and of finite groups, this paper will go through two standard examples, the Lie algebra sl2C and the finite group Sn, to illustrate techniques for their construction and use. In addition, those examples will develop some important theory behind representations of Lie algebras and...
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How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers ; and there remain practical difficulties even for groups of relatively small orders ( á 100). The present ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.08.011