Let Cp denote the cyclic group of order p where p ≥ 3 is prime. We denote by Vn the indecomposable n dimensional representation of Cp over a field F of characteristic p. We compute a set of generators, in fact a SAGBI basis, for the ring of invariants F[V2 ⊕ V2 ⊕ V3]p .

We introduce canonical bases for subalgebras of quotients of the commutative and non-commutative polynomial ring. The usual theory for Gröbner bases and its counterpart for subalgebras of polynomial rings, also called SAGBI bases, are combined to obtain a tool for computation in subalgebras of factor algebras.

In this paper we examine subalgebras on two generators in the univariate polynomial ring. A set, S, of polynomials in a subalgebra of a polynomial ring is called a canonical basis (also referred to as SAGBI basis) for the subalgebra if all lead monomials in the subalgebra are products of lead monomials of polynomials in S. In this paper we prove that a pair of polynomials {f, g} is a canonical ...

We present families of tableaux which interpolate between the classical semi-standard Young and matching field tableaux. Algebraically, this corresponds to SAGBI bases Plücker algebras . show that each such family leads a toric ideal, can be realized as initial hence degeneration for flag variety.

Let k be a field and G be a finite subgroup of GLn(Z). We show that the ring of multiplicative invariants k[x±1 1 , . . . , x ±1 n ] G has a finite SAGBI basis if and only if G is generated by reflections.

The maximal minors of a p× (m+p)-matrix of univariate polynomials of degree n with indeterminate coefficients are themselves polynomials of degree np. The subalgebra generated by their coefficients is the coordinate ring of the quantum Grassmannian, a singular compactification of the space of rational curves of degree np in the Grassmannian of p-planes in (m + p)-space. These subalgebra generat...