Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tridiagonal pairs of $q$-Serre type and their linear perturbations   A tridiagonal pair is an ordered pair of diagonalizable linear maps on a
nonzero finite-dimensional vector space, that each act on the eigenspaces of
the other in a block-tridiagonal fashion. We consider a tridiagonal pair $(A,
A^*)$ of $q$-Serre type; for such a pair the maps $A$ and $A^*$ satisfy the
$q$-Serre relations. There is a linear map $K$ in the literature that is used
to describe how $A$ and $A^*$ are related. We investigate a pair of linear maps
$B=A$ and $B^* = tA^* + (1-t)K$, where $t$ is any scalar. Our goal is to find a
necessary and sufficient condition on $t$ for the pair $(B, B^*)$ to be a
tridiagonal pair. We show that $(B, B^*)$ is a tridiagonal pair if and only if
$t \neq 0$ and $P \bigl( t(q-q^{-1})^{-2} \bigr)\not=0$, where $P$ is a certain
polynomial attached to $(A, A^*)$ called the Drinfel'd polynomial.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an