Olshansky Centralizer Construction in Deligne Tensor Categories

Student: Utiralova Aleksandra

Supervisor: Leonid Grigoryevich Rybnikov

Educational Programme: Mathematics and Mathematical Physics (Master)

Year of Graduation: 2019

In this work we introduce and prove the generalization of Olshanski's centralizer construction of the Yangian Y(gl_n). Namely, we prove that for generic complex parameter t the centralizer subalgebra of GL_t-invariants in the universal enveloping algebra U(gl_{t+n}) is the tensor product of Y({gl_n) and the center of U(gl_t). The main feature of this construction is that it does not involve passing to a limit, contrary to the original construction of Olshanski.

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