We consider the rings of invariants $R^G$, where $R$ is the symmetric algebra of a tensor product between two vector spaces over the field $F_p$ and $G=U_n\times U_m$. A polynomial algebra is constructed and these invariants provide Chern classes for the modular cohomology of $U_{n+m}$.

Keywords:

Invariant theory, cohomology of the unipotent group Invariant theory, cohomology of the unipotent group

MSC Classifications:

13F20 show english descriptions Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] 13F20 - Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]

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