Young Tables and Monodromy of Bethe Vectors

Student: Levin Ilya

Supervisor: Leonid Grigoryevich Rybnikov

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2018

In this paper we calculate monodromy of eigenvectors of Gaudin hamiltonians in group algebra for symmetric group. Concretly, eigenvectors for limit subalgebras are numbered by the standard tableaux. We express monodromy as composition of elementary transformations $\gamma^k$: $\gamma^k$ permutes $k$-th and $k+1$-th boxes of the tableau, if they are not adjacent, or does nothing in the opposite case. Our main result is describing of the monodromy of the cactus group generator $s_{1, q}$ as $(\gamma^2 \circ \ldots \circ \gamma^{q-1}) \circ (\gamma^2 \circ \ldots \circ \gamma^{q-2} )\circ \ldots \circ (\gamma^2 \circ \gamma^3) \circ (\gamma^2)$.

Full text (added June 3, 2018)

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