## Advanced Studies in Pure Mathematics

### Length Functions for $G(r, p, n)$

Toshiaki Shoji

#### Abstract

In this paper, we construct a length function $n(w)$ for the complex reflection group $W = G(r, p, n)$ by making use of certain partitions of the root system associated to $\widetilde{W} = G(r, 1, n)$. We show that the function $n(w)$ yields the Poincaré polynomial $P_W(q)$. We give some characterization of this function in a way independent of the choice of the root system.

#### Article information

Dates
First available in Project Euclid: 20 August 2018

https://projecteuclid.org/ euclid.aspm/1534789266

Digital Object Identifier
doi:10.2969/aspm/02810327

Mathematical Reviews number (MathSciNet)
MR1864487

Zentralblatt MATH identifier
0986.20039

#### Citation

Shoji, Toshiaki. Length Functions for $G(r, p, n)$. Combinatorial Methods in Representation Theory, 327--342, Mathematical Society of Japan, Tokyo, Japan, 2000. doi:10.2969/aspm/02810327. https://projecteuclid.org/euclid.aspm/1534789266