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Yangian for gl2 and Gelfand-Tsetlin basis for gln
Abstract
We construct an explicit realization of finite-dimensional irreducible representations Vλ of gln using the representation theory of Y(gl2). We consider Vλ as the evaluation representation of Y(gln) and restrict it to the subalgebras Y(gl2)(i). Then Vλ is completely reducible as a representation of Y(gl2)(i). It allows us to use the explicit formulas for irreducible representations of Y(gl2).
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BibTeX
@misc{belov2026yangian,
title = {{Yangian for $\mathfrakgl_2$ and Gelfand-Tsetlin basis for $\mathfrakgl_n$}},
author = {Mark Belov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14273},
eprint = {2610.14273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14273},
}
RIS
TY - UNPB
TI - Yangian for gl_2 and Gelfand-Tsetlin basis for gl_n
AU - Mark Belov
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14273
UR - https://arxiv.org/abs/2610.14273
AB - We construct an explicit realization of finite-dimensional irreducible representations V_λ of gl_n using the representation theory of Y(gl_2). We consider V_λ as the evaluation representation of Y(gl_n) and restrict it to the subalgebras Y(gl_2)^(i). Then V_λ is completely reducible as a representation of Y(gl_2)^(i). It allows us to use the explicit formulas for irreducible representations of Y(gl_2).
ER -