Centralizers of the superalgebra <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mstyle> <mml:mrow> <mml:mi>o</mml:mi> <mml:mi>s</mml:mi> <mml:mi>p</mml:mi> </mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mstyle> </mml:math> : the Brauer algebra as a quotient of the Bannai–Ito algebra <sup>*</sup>
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Bibliographic record
Abstract
Abstract We provide an explicit isomorphism between a quotient of the Bannai–Ito algebra and the Brauer algebra. We clarify also the connection with the action of the Lie superalgebra on the threefold tensor product of its fundamental representation. Finally, a conjecture is proposed to describe the centralizer of acting on three copies of an arbitrary finite irreducible representation in terms of a quotient of the Bannai–Ito algebra.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.005 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.129 | 0.001 |
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