Schubert polynomials for the affine Grassmannian of the symplectic group
نویسندگان
چکیده
منابع مشابه
Schubert Polynomials for the Affine Grassmannian of the Symplectic Group
We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur’s P and Q functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine typ...
متن کاملSchubert Polynomials for the Affine Grassmannian
Confirming a conjecture of Mark Shimozono, we identify polynomial representatives for the Schubert classes of the affine Grassmannian as the k-Schur functions in homology and affine Schur functions in cohomology. Our results rely on Kostant and Kumar’s nilHecke ring, work of Peterson on the homology of based loops on a compact group, and earlier work of ours on non-commutative k-Schur functions.
متن کاملK-theory Schubert calculus of the affine Grassmannian
We construct the Schubert basis of the torus-equivariant K-homology of the affine Grassmannian of a simple algebraic group G, using the K-theoretic NilHecke ring of Kostant and Kumar. This is the K-theoretic analogue of a construction of Peterson in equivariant homology. For the case where G= SLn, the K-homology of the affine Grassmannian is identified with a sub-Hopf algebra of the ring of sym...
متن کاملa note on the affine subgroup of the symplectic group
we examine the symplectic group $sp_{2m}(q)$ and its correspondingaffine subgroup. we construct the affine subgroup and show that itis a split extension. as an illustration of the above we study theaffine subgroup $2^5{:}sp_4(2)$ of the group $sp_6(2)$.
متن کاملstudy of cohesive devices in the textbook of english for the students of apsychology by rastegarpour
this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...
ذخیره 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: Mathematische Zeitschrift
سال: 2009
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-009-0488-9