In algebraic geometry, standard monomial theory describes the sections of a line bundle over a generalized flag variety or Schubert variety of a reductive...

Riemann surface.He also introduced and named the concept called Standard monomial theory. He was a recipient of the Padma Bhushan in 2009, the third highest...

Grassmannians. It is now a part of representation theory called standard monomial theory. The idea of standard basis in the universal enveloping algebra of...

Indian mathematician at the University of Hyderabad who developed standard monomial theory in collaboration with his PhD supervisor C. S. Seshadri. Musili...

representation theory, who introduced the Littelmann path model and used it to solve several conjectures in standard monomial theory and other areas...

sequence of monomials is finite. Although Gröbner basis theory does not depend on a particular choice of an admissible monomial ordering, three monomial orderings...

Demazure's conjecture (for classical groups) follows from their work on standard monomial theory, and Peter Littelmann extended this to all reductive algebraic...

Indian math student S. P. Sundaram. Standard monomial theory, C. S. Seshadri introduced a concept named Standard Monomials in 1978. Basu's theorem – The Basu's...

representation theory, standard Young tableaux of size k describe bases in irreducible representations of the symmetric group on k letters. The standard monomial basis...

it has no nil one-sided ideal other than { 0 } {\displaystyle \{0\}} . Monomial conjecture on Noetherian local rings Existence of perfect cuboids and associated...

of good filtrations for these tensor products also follows from standard monomial theory. Donkin, Stephen (1985), Rational representations of algebraic...

depending on the evaluation of the basis functions at the data points). The monomial basis for the vector space of analytic functions is given by { x n ∣ n...

ideas is given by the theory of standard monomials. Simple examples of invariant theory come from computing the invariant monomials from a group action...

a monomial does not change the order of the terms. For Gröbner bases, a further condition must be satisfied, namely that every non-constant monomial is...

bridge between the theory of crystal bases arising from the work of Kashiwara and Lusztig on quantum groups and the standard monomial theory of C. S. Seshadri...

variables X1, ..., Xn, written hk for k = 0, 1, 2, ..., is the sum of all monomials of total degree k in the variables. Formally, h k ( X 1 , X 2 , … , X...

a domain. This may be proved using an ordering on the noncommutative monomials. If R is a domain and S is an Ore extension of R then S is a domain. The...

suspected that Co0 was transitive on Λ2, and indeed he found a new matrix, not monomial and not an integer matrix. Let η be the 4-by-4 matrix 1 2 ( 1 − 1 − 1 −...

one dimensional representation is called a monomial representation, because it can be represented as monomial matrices. Some groups have the property that...

in J (usual sum of vectors). In particular, the product of two monomials is a monomial whose exponent vector is the sum of the exponent vectors of the...

refers to the standard basis defined by the Kronecker delta. In a polynomial ring, it refers to its standard basis given by the monomials, ( X i ) i {\displaystyle...

This part of precalculus prepares the student for integration of the monomial x p {\displaystyle x^{p}} in the instance of p = − 1 {\displaystyle p=-1}...

number of standard Young tableaux whose shape is a given Young diagram. It has applications in diverse areas such as representation theory, probability...

check this for monomials in the ei's. Now, a monomial of even degree commutes with every element. Therefore if either x or y is a monomial of even degree...

integral over a monomial of coordinates x i {\displaystyle x_{i}} and fields ϕ i {\displaystyle \phi _{i}} . Examples are the standard ϕ 4 {\displaystyle...

{\displaystyle g_{1},\dots ,g_{p}} are monomials. In the context of geometric programming (unlike standard mathematics), a monomial is a function from R + + n {\displaystyle...

),} where V(φ) is a potential term, often taken to be a polynomial or monomial of degree 3 or higher. The action functional is S ( ϕ ) = ∫ L ( ϕ ) d x...

different terminology and notation for continued fraction. In number theory the standard unqualified use of the term continued fraction refers to the special...

completeness) The algebraic degree of a function is the order of the highest order monomial in its algebraic normal form Circuit complexity attempts to classify Boolean...

distributive law to the product. This expands the product into a sum of monomials of the form x a 1 x 2 a 2 x 3 a 3 ⋯ {\displaystyle x^{a_{1}}x^{2a_{2}}x^{3a_{3}}\cdots...