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Hi everyone. My recent work has me developing software to compute in $H^\ast(G/P)$, where $G$ is a complex connected semisimple algebraic group and $P$ is a standard parabolic subgroup (usually, $B$ or a maximal $P$). While my programs are built on sound theory, one can never be to too sure. It's always good practice to check your work.

I'm looking for references of multiplication tables of these cohomology rings.

In particular, I'm interested in cases where $G$ is NOT simply-laced (that is, Lie type $B_n$, $C_n$, $F_4$, $G_2$), though simply-laced tables would be nice too. Any tables would depend on a choice of additive basis for $H^\ast(G/P)$. I typically use cohomology classes either Hom-dual or Poincare dual to the usual Schubert varieties living in $G/P$, and I like to parameterize my Schubert varieties with $W^P$, the minimal length coset representatives of $W/W_P$ where $W$ is the Weyl group and $W_P$ is the Weyl group of the Levi associated to $P$. Tables using this convention would be great. Of course, tables in any basis would be fine. :D

Thanks so much.

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# Multiplication tables for H*(G/P)?

Hi everyone. My recent work has me developing software to compute in $H^\ast(G/P)$, where $G$ is a complex connected semisimple algebraic group and $P$ is a standard parabolic subgroup (usually, $B$ or a maximal $P$). While my programs are built on sound theory, one can never be to sure. It's always good practice to check your work.

I'm looking for references of multiplication tables of these cohomology rings.

In particular, I'm interested in cases where $G$ is NOT simply-laced (that is, Lie type $B_n$, $C_n$, $F_4$, $G_2$), though simply-laced tables would be nice too. Any tables would depend on a choice of additive basis for $H^\ast(G/P)$. I typically use cohomology classes either Hom-dual or Poincare dual to the usual Schubert varieties living in $G/P$, and I like to parameterize my Schubert varieties with $W^P$, the minimal length coset representatives of $W/W_P$ where $W$ is the Weyl group and $W_P$ is the Weyl group of the Levi associated to $P$. Tables using this convention would be great. Of course, tables in any basis would be fine. :D

Thanks so much.