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The classical Pieri formula gives a combinatorial rule for decomposing the product of a Schur function and a complete homogeneous symmetric polynomial as a linear combination of Schur functions with integer coefficients. We give a Pieri rule for describing the product of an orthosymplectic character and an orthosymplectic character arising from a one-row partition. We establish that the orthosymplectic Pieri rule coincides with Sundarams Pieri rule for symplectic characters and that orthosymplectic characters and symplectic characters obey the same product rule.
We prove the affine Pieri rule for the cohomology of the affine flag variety conjectured by Lam, Lapointe, Morse and Shimozono. We study the cap operator on the affine nilHecke ring that is motivated by Kostant and Kumars work on the equivariant coho
The Pieri rule gives an explicit formula for the decomposition of the tensor product of irreducible representation of the complex general linear group GL(n,C) with a symmetric power of the standard representation on C^n. It is an important and long u
We explore monoids generated by operators on certain infinite partial orders. Our starting point is the work of Fomin and Greene on monoids satisfying the relations $(u{r}+u{r+1})u{r+1}u{r}=u{r+1}u{r}(u{r}+u{r+1})$ and $u{r}u{t}=u{s}u{r}$ if $|r-t|>1
In this note, a new concept called {em $SDR$-matrix} is proposed, which is an infinite lower triangular matrix obeying the generalized rule of David star. Some basic properties of $SDR$-matrices are discussed and two conjectures on $SDR$-matrices are
We give a complete description of the finite-dimensional irreducible representations of the Yangian associated with the orthosymplectic Lie superalgebra $frak{osp}_{1|2}$. The representations are parameterized by monic polynomials in one variable, th