Representations of Quantum Algebras and Combinatorics of Young Tableaux - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representations of Quantum Algebras and Combinatorics of Young Tableaux write by Susumu Ariki. This book was released on 2002. Representations of Quantum Algebras and Combinatorics of Young Tableaux available in PDF, EPUB and Kindle. This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups. Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and toapply the theory to representations of Hecke algebras. The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A {r-1 {(1) $ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be thecombinatorics of Young tableaux. The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type. The book is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups and quantum groups, the theory of Hecke algebras, algebraic combinatorics, andrelated fields.
Representations of quantum algebras and combinatorics of Young tableaux
Representations of quantum algebras and combinatorics of Young tableaux - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representations of quantum algebras and combinatorics of Young tableaux write by Susumu Ariki. This book was released on 2002. Representations of quantum algebras and combinatorics of Young tableaux available in PDF, EPUB and Kindle.
Combinatorial and Geometric Representation Theory
Combinatorial and Geometric Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Combinatorial and Geometric Representation Theory write by Seok-Jin Kang. This book was released on 2003. Combinatorial and Geometric Representation Theory available in PDF, EPUB and Kindle. This volume presents the proceedings of the international conference on Combinatorial and Geometric Representation Theory. In the field of representation theory, a wide variety of mathematical ideas are providing new insights, giving powerful methods for understanding the theory, and presenting various applications to other branches of mathematics. Over the past two decades, there have been remarkable developments. This book explains the strong connections between combinatorics, geometry, and representation theory. It is suitable for graduate students and researchers interested in representation theory.
Physical Combinatorics
Physical Combinatorics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Physical Combinatorics write by Masaki Kashiwara. This book was released on 2012-12-06. Physical Combinatorics available in PDF, EPUB and Kindle. Taking into account the various criss-crossing among mathematical subject, Physical Combinatorics presents new results and exciting ideas from three viewpoints; representation theory, integrable models, and combinatorics. This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Recent developments in integrable models reveal an unexpected link between representation theory and statistical mechanics through combinatorics.
Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry
Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry write by Vlastimil Dlab. This book was released on . Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry available in PDF, EPUB and Kindle. These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
