k-Schur Functions and Affine Schubert Calculus

k-Schur Functions and Affine Schubert Calculus
Author :
Publisher : Springer
Total Pages : 226
Release :
ISBN-10 : 9781493906826
ISBN-13 : 1493906828
Rating : 4/5 (26 Downloads)

Book Synopsis k-Schur Functions and Affine Schubert Calculus by : Thomas Lam

Download or read book k-Schur Functions and Affine Schubert Calculus written by Thomas Lam and published by Springer. This book was released on 2014-06-05 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.


k-Schur Functions and Affine Schubert Calculus Related Books

k-Schur Functions and Affine Schubert Calculus
Language: en
Pages: 226
Authors: Thomas Lam
Categories: Mathematics
Type: BOOK - Published: 2014-06-05 - Publisher: Springer

DOWNLOAD EBOOK

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the cur
K-Schur Functions and Affine Schubert Calculus
Language: en
Pages: 228
Authors: Thomas Lam
Categories:
Type: BOOK - Published: 2014-06-30 - Publisher:

DOWNLOAD EBOOK

Facets of Algebraic Geometry: Volume 2
Language: en
Pages: 396
Authors: Paolo Aluffi
Categories: Mathematics
Type: BOOK - Published: 2022-04-07 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the second of a pair) present substantial contributions to algebrai
The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions
Language: en
Pages: 113
Authors: Thomas Lam
Categories: Mathematics
Type: BOOK - Published: 2013-04-22 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes
Recent Trends in Algebraic Combinatorics
Language: en
Pages: 364
Authors: Hélène Barcelo
Categories: Mathematics
Type: BOOK - Published: 2019-01-21 - Publisher: Springer

DOWNLOAD EBOOK

This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing