Resumen de Skew representations of twisted Yangians

Alexander Molev

• 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) on the space of homomorphisms HomgM (W, V ), where W and V are finite-dimensional irreducible modules over gM and gN , respectively. In the symplectic case these representations turn out to be irreducible and we identify them by calculating the corresponding Drinfeld polynomials. We also apply the quantum Sylvester theorem to realize the twisted Yangian as a projective limit of certain centralizers in universal enveloping algebras.