From Parking Functions to Gelfand Pairs

Details From Parking Functions to Gelfand Pairs From Parking Functions to Gelfand Pairs

2010-02-08

arxiv.org/abs/1002.1519v2

Mathematics

Combinatorics

14 pages, 1 figure

Scientific paper

A pair $(G,K)$ of a group and its subgroup is called a Gelfand pair if the induced trivial representation of $K$ on $G$ is multiplicity free. Let $(a_j)$ be a sequence of positive integers of length $n$, and let $(b_i)$ be its non-decreasing rearrangement. The sequence $(a_i)$ is called a parking function of length $n$ if $b_i \leq i$ for all $i=1,\...,n$. In this paper we study certain Gelfand pairs in relation with parking functions. In particular, we find explicit descriptions of the decomposition of the associated induced trivial representations into irreducibles. We obtain and study a new $q$ analogue of the Catalan numbers $\frac{1}{n+1}{2n \choose n}$, $n\geq 1$.

Affiliated with

Also associated with

No associations

Rating

From Parking Functions to Gelfand Pairs 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 From Parking Functions to Gelfand Pairs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From Parking Functions to Gelfand Pairs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-307673