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(Institute for High Energy Physics, Protvino, Russia & Higher School of Economics, Faculty of Mathematics, Moscow, Russia)
Amphithéâtre Léon Motchane (IHES)
Amphithéâtre Léon Motchane
35, route de Chartres, F-91440 Bures-sur-Yvette (France)
: In my talk I consider a q-deformation of the so-called Yangian Y(gl(m)). The standard Yangian Y(gl(m)) (associated with the Yang R-matrix) was introduced by V.Drinfeld and is rather well known. It possesses a lot of interesting properties and has applications in integrable models of mathematical physics (for example, in the non-linear Schroedinger model), W-algebras and so on. Its q-analog, called the q-Yangian, is usually defined as a "half" of a quantum affine group. D. Gurevich and me suggest a new construction for such a q-analog of the Yangian Y(gl(m)). We call it "braided Yangian". We associate the braided Yangians with rational and trigonometric quantum R-matrices, depending on a formal parameter. These R-matrices arise from constant involutive or Hecke R-matrices by means of the Baxterization procedure. Our braided Yangians admit the evaluation morphism onto quantum matrix algebras and due to this one can construct a rich representation theory for them. In my talk I also plan to define analogs of symmetric polynomials (full, elementary and powers sums) which form a commutative subalgebra in the braided Yangian and exibit some noncommutative matrix identities similar to the Newton-Cayley-Hamilton identities of the classical matrix anlysis.