A duality between pairs of split decompositions for a Q-polynomial distance-regular graph

作者：Kim Joohyung^*

来源：Discrete Mathematics, 2010, 310(12): 1828-1834.

DOI：10.1016/j.disc.2010.01.004

• Distance-regular graph
• Tridiagonal pair
• Subconstituent algebra
• Split decomposition

Let Gamma denote a Q-polynomial distance-regular graph with diameter D >= 3 and standard module V. Recently, Ito and Terwilliger introduced four direct sum decompositions of V; we call these the (mu, nu)-split decompositions of V, where mu, nu is an element of {down arrow, up arrow}. In this paper we show that the (down arrow, down arrow)-split decomposition and the (up arrow, up arrow)-split decomposition are dual with respect to the standard Hermitian form on V. We also show that the (down arrow, up arrow)-split decomposition and the (up arrow, down arrow)-split decomposition are dual with respect to the standard Hermitian form on V.

• 出版日期2010-6-28