Let G be type B_2 and denote the two simple roots a and β with α the short one. If B is a Borel subgroup of G, X a character of B, and(X) a induced line bundle on G/B, we denote by H^1 (X)=H^1 (G/B, (X)) the first c...Let G be type B_2 and denote the two simple roots a and β with α the short one. If B is a Borel subgroup of G, X a character of B, and(X) a induced line bundle on G/B, we denote by H^1 (X)=H^1 (G/B, (X)) the first cohomology group of (X). Our main results in this paperare: Theorem Let G be type B_2;x∈X(T) be p-regular and 1≤a<p. Then H^1(X) is a simple G-module iff one of the following conditions Ⅰ)-Ⅳ> holds: Ⅰ) X∈s_α·C_0 Ⅱ) X∈s_β·C_0 Ⅲ) Ⅳ)展开更多
文摘Let G be type B_2 and denote the two simple roots a and β with α the short one. If B is a Borel subgroup of G, X a character of B, and(X) a induced line bundle on G/B, we denote by H^1 (X)=H^1 (G/B, (X)) the first cohomology group of (X). Our main results in this paperare: Theorem Let G be type B_2;x∈X(T) be p-regular and 1≤a<p. Then H^1(X) is a simple G-module iff one of the following conditions Ⅰ)-Ⅳ> holds: Ⅰ) X∈s_α·C_0 Ⅱ) X∈s_β·C_0 Ⅲ) Ⅳ)
