Affine Insertion And Pieri Rules For The Affine Grassmannian
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| Author | : Thomas Lam |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 103 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821846582 |
Download Affine Insertion and Pieri Rules for the Affine Grassmannian Book in PDF, Epub and Kindle
The authors study combinatorial aspects of the Schubert calculus of the affine Grassmannian ${\rm Gr}$ associated with $SL(n,\mathbb{C})$.Their main results are: Pieri rules for the Schubert bases of $H^*({\rm Gr})$ and $H_*({\rm Gr})$, which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. A new combinatorial definition for $k$-Schur functions, which represent the Schubert basis of $H_*({\rm Gr})$. A combinatorial interpretation of the pairing $H^*({\rm Gr})\times H_*({\rm Gr}) \rightarrow\mathbb Z$ induced by the cap product.
| Author | : Thomas Lam |
| Publisher | : |
| Total Pages | : 82 |
| Release | : 2010 |
| Genre | : MATHEMATICS |
| ISBN | : 9781470405915 |
Download Affine Insertion and Pieri Rules for the Affine Grassmannian Book in PDF, Epub and Kindle
| Author | : |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 103 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 0821867180 |
Download Affine Insertion and Pieri Rules for the Affine Grassmannian Book in PDF, Epub and Kindle
"Volume 208, number 977 (second of 6 numbers)."
| Author | : Thomas Lam |
| Publisher | : Springer |
| Total Pages | : 226 |
| Release | : 2014-06-05 |
| Genre | : Mathematics |
| ISBN | : 1493906828 |
Download k-Schur Functions and Affine Schubert Calculus Book in PDF, Epub and Kindle
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.
| Author | : Thomas Lam |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 113 |
| Release | : 2013-04-22 |
| Genre | : Mathematics |
| ISBN | : 082187294X |
Download The Poset of $k$-Shapes and Branching Rules for $k$-Schur Functions Book in PDF, Epub and Kindle
The authors give a combinatorial expansion of a Schubert homology class in the affine Grassmannian $\mathrm{Gr}_{\mathrm{SL}_k}$ into Schubert homology classes in $\mathrm{Gr}_{\mathrm{SL}_{k+1}}$. This is achieved by studying the combinatorics of a new class of partitions called $k$-shapes, which interpolates between $k$-cores and $k+1$-cores. The authors define a symmetric function for each $k$-shape, and show that they expand positively in terms of dual $k$-Schur functions. They obtain an explicit combinatorial description of the expansion of an ungraded $k$-Schur function into $k+1$-Schur functions. As a corollary, they give a formula for the Schur expansion of an ungraded $k$-Schur function.
| Author | : Mahir Can |
| Publisher | : Springer |
| Total Pages | : 360 |
| Release | : 2014-06-11 |
| Genre | : Mathematics |
| ISBN | : 149390938X |
Download Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics Book in PDF, Epub and Kindle
This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: structure and representation theory of reductive algebraic monoids monoid schemes and applications of monoids monoids related to Lie theory equivariant embeddings of algebraic groups constructions and properties of monoids from algebraic combinatorics endomorphism monoids induced from vector bundles Hodge–Newton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly π-regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.
| Author | : Ernst Heintze |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 81 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821869183 |
Download Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category Book in PDF, Epub and Kindle
Heintze and Gross discuss isomorphisms between smooth loop algebras and of smooth affine Kac-Moody algebras in particular, and automorphisms of the first and second kinds of finite order. Then they consider involutions of the first and second kind, and make the algebraic case. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
| Author | : Hélène Barcelo |
| Publisher | : Springer |
| Total Pages | : 362 |
| Release | : 2019-01-21 |
| Genre | : Mathematics |
| ISBN | : 3030051412 |
Download Recent Trends in Algebraic Combinatorics Book in PDF, Epub and Kindle
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.
| Author | : Tom H. Koornwinder |
| Publisher | : Cambridge University Press |
| Total Pages | : 442 |
| Release | : 2020-10-15 |
| Genre | : Mathematics |
| ISBN | : 1108916554 |
Download Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions Book in PDF, Epub and Kindle
This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.
| Author | : Kang-Tae Kim |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 126 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 0821849654 |
Download Robin Functions for Complex Manifolds and Applications Book in PDF, Epub and Kindle
"Volume 209, number 984 (third of 5 numbers)."
