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- W2000759958 abstract "Let (Γ,⪰) be a finite poset. The set Z⩾0Γ,⪰ of all order preserving functions f:Γ→Z⩾0 forms a semigroup, and is called a Hibi cone. It has a simple structure and has been used to describe the structure of some algebras of interest in representation theory. Now for A, B⊆Γ, we consider the setΩA,B(Γ):={f∈ZΓ,⪰:f(A)⩾0,f(B)⩽0}. It is also a semigroup. We call it a sign Hibi cone. We will develop the structure theory for the sign Hibi cones. Next, we construct an algebra An,k,l whose structure encodes the decomposition of tensor productρ⊗Sα1(Cn⁎)⊗⋯⊗Sαl(Cn⁎) where ρ is a polynomial representation of GLn and Sαi(Cn⁎) is the αith symmetric power of Cn⁎, the dual of the standard representation of GLn on Cn. We call An,k,l an anti-row iterated Pieri algebra for GLn. We show that a certain sign Hibi cone Ωn,k,l is naturally associated with An,k,l and we construct a basis for An,k,l indexed by the elements of Ωn,k,l. We further show that this basis contains all the standard monomials on a set of algebra generators of An,k,l." @default.
- W2000759958 created "2016-06-24" @default.
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- W2000759958 date "2014-07-01" @default.
- W2000759958 modified "2023-09-29" @default.
- W2000759958 title "Sign Hibi cones and the anti-row iterated Pieri algebras for the general linear groups" @default.
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- W2000759958 doi "https://doi.org/10.1016/j.jalgebra.2014.01.039" @default.
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