Schubert Calculus via Hasse-Schmidt Derivations
نویسندگان
چکیده
منابع مشابه
Schubert Calculus via Hasse-schmidt Derivations
A natural Hasse-Schmidt derivation on the exterior algebra of a free module realizes the (small quantum) cohomology ring of the grassmannian Gk(C ) as a ring of operators on the exterior algebra of a free module of rank n. Classical Pieri’s formula can be interpreted as Leibniz’s rule enjoyed by special Schubert cycles with respect to the wedge product.
متن کاملJets via Hasse-schmidt Derivations
This preprint is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of projectivized jet spaces (as in Green and Griffiths [G-G]) is included. This paper contains a few brief notes on how to define jets using Hasse-Schmidt ...
متن کاملHasse–Schmidt derivations, divided powers and differential smoothness
Let k be a commutative ring, A a commutative k-algebra and D the filtered ring of k-linear differential operators of A. We prove that: (1) The graded ring grD admits a canonical embedding θ into the graded dual of the symmetric algebra of the module ΩA/k of differentials of A over k, which has a canonical divided power structure. (2) There is a canonical morphism θ from the divided power algebr...
متن کاملHasse-Schmidt Derivations and the Hopf Algebra of Non-Commutative Symmetric Functions
Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): NSymm=Z 1 2 , ,... Z Z . It is shown that an associative algebra A with a Hasse-Schmidt derivation 1 2 ( , , ,...) d id d d on it is exactly the same as an NSymm module algebra. The primitives of NSymm act as ordinary derivations. There are many formulas for the generators Zi in terms ...
متن کاملElliptic Schubert Calculus via Formal Root Polynomials
An important combinatorial result in equivariant cohomology and K-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work uniformly in all Lie types, and are based on the concept of a root polynomial. In this paper we define formal root polynomials associated with an arbitrary formal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2005
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2005.v9.n3.a2