The Drinfel'd polynomial of a tridiagonal pair
Tatsuro Ito, Paul Terwilliger

TL;DR
This paper introduces the Drinfel'd polynomial associated with a sharp tridiagonal pair, establishing its invariance properties and connection to classical Lie algebra and quantum group polynomials, with potential applications in classification.
Contribution
It defines the Drinfel'd polynomial for sharp tridiagonal pairs, proves its invariance under certain transformations, and relates it to classical algebraic structures.
Findings
The Drinfel'd polynomial is invariant under specific transformations.
Roots of the polynomial are computed for a special case.
The polynomial relates to classical Lie algebra and quantum group theory.
Abstract
Let denote a field and let denote a vector space over with finite positive dimension. We consider a pair of linear transformations and that satisfy the following conditions: (i) each of is diagonalizable; (ii) there exists an ordering of the eigenspaces of such that for , where and ; (iii) there exists an ordering of the eigenspaces of such that for , where and ; (iv) there is no subspace of such that , , , . We call such a pair a {\it tridiagonal pair} on . It is known that and for the dimensions of ,…
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Taxonomy
TopicsFinite Group Theory Research · Matrix Theory and Algorithms · graph theory and CDMA systems
