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SUMMARY:Braided Yangians
DTSTART;VALUE=DATE-TIME:20170117T133000Z
DTEND;VALUE=DATE-TIME:20170117T150000Z
DTSTAMP;VALUE=DATE-TIME:20201025T060702Z
UID:indico-event-1906@indico.math.cnrs.fr
DESCRIPTION:: In my talk I consider a q-deformation of the so-called Yangi
an Y(gl(m)). The standard Yangian Y(gl(m)) (associated with the Yang R-mat
rix) was introduced by V.Drinfeld and is rather well known. It possesses a
lot of interesting properties and has applications in integrable models o
f mathematical physics (for example\, in the non-linear Schroedinger model
)\, W-algebras and so on. Its q-analog\, called the q-Yangian\, is usuall
y defined as a "half" of a quantum affine group. D. Gurevich and me sugges
t 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 mor
phism onto quantum matrix algebras and due to this one can construct a ric
h 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 noncommut
ative matrix identities similar to the Newton-Cayley-Hamilton identities o
f the classical matrix anlysis.\n\nhttps://indico.math.cnrs.fr/event/1906/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/1906/
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