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- W2912171130 abstract "We elaborate on the recent observation that evolution for twist knots simplifies when described in terms of triangular evolution matrix ${cal B}$, not just its eigenvalues $Lambda$, and provide a universal formula for ${cal B}$, applicable to arbitrary rectangular representation $R=[r^s]$. This expression is in terms of skew characters and it remains literally the same for the 4-graded rectangularly-colored hyperpolynomials, if characters are substituted by Macdonald polynomials. Due to additional factorization property of the differential-expansion coefficients for the double-braid knots, explicit knowledge of twist-family evolution leads to a nearly explicit answer for Racah matrix $bar S$ in arbitrary rectangular representation $R$. We also relate matrix evolution to existence of a peculiar rotation $U$ of Racah matrix, which diagonalizes the $Z$-factors in the differential expansion -- what can be a key to further generalization to non-rectangular representations $R$." @default.
- W2912171130 created "2019-02-21" @default.
- W2912171130 creator A5075669127 @default.
- W2912171130 date "2019-06-01" @default.
- W2912171130 modified "2023-10-14" @default.
- W2912171130 title "On exclusive Racah matrices <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mover accent=true><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy=false>¯</mml:mo></mml:mrow></mml:mover></mml:math> for rectangular representations" @default.
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- W2912171130 doi "https://doi.org/10.1016/j.physletb.2019.04.034" @default.
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