Tridiagonal pairs of Krawtchouk type

Details Tridiagonal pairs of Krawtchouk type Tridiagonal pairs of Krawtchouk type

2007-06-07

arxiv.org/abs/0706.1065v1

Mathematics

Rings and Algebras

20 pages

Scientific paper

Let $K$ denote an algebraically closed field with characteristic 0 and let $V$ denote a vector space over $K$ with finite positive dimension. Let $A,A^*$ denote a tridiagonal pair on $V$ with diameter $d$. We say that $A,A^*$ has Krawtchouk type whenever the sequence $\lbrace d-2i\rbrace_{i=0}^d$ is a standard ordering of the eigenvalues of $A$ and a standard ordering of the eigenvalues of $A^*$. Assume $A,A^*$ has Krawtchouk type. We show that there exists a nondegenerate symmetric bilinear form $< , >$ on $V$ such that $= < u,Av>$ and $= < u,A^*v>$ for $u,v\in V$. We show that the following tridiagonal pairs are isomorphic: (i) $A,A^*$; (ii) $-A,-A^*$; (iii) $A^*,A$; (iv) $-A^*,-A$. We give a number of related results and conjectures.

Affiliated with

Also associated with

No associations

Rating

Tridiagonal pairs of Krawtchouk type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tridiagonal pairs of Krawtchouk type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tridiagonal pairs of Krawtchouk type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-442493