lie-algebras-and-their-representations

Source code for my notes on representations of semisimple Lie algebras and Olivier Mathieu's classification of simple weight modules

Name	Size	Mode
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references.bib	5169B	-rw-r--r--

@book{serganova,
  title =     {A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras},
  author =    {Gruson, Caroline and Serganova, Vera},
  year =      {2018},
}

@book{fulton-harris,
  title =     {Representation Theory: A First Course},
  author =    {Fulton, William and Harris, Joe},
  publisher = {Springer},
  year =      {1991},
  series =    {Graduate Texts in Mathematics / Readings in Mathematics},
  edition =   {Corrected},
}

@book{etingof,
  title =     {Introduction to Representation Theory},
  author =    {Etingof, Pavel and Golberg, Oleg and Hensel, Sebastian and Liu, Tiankai and Schwendner, Alex  and Vaintrob, Dmitry and Yudovina, Elena},
  publisher = {American Mathematical Society},
  year =      {2011},
  series =    {Student Mathematical Library},
}

@book{kirillov,
  title =     {Introduction to Lie Groups and Lie Algebras},
  author =    {Kirillov, Alexander},
  edition =   {Preliminary version},
  year =      {2008},
  url =       {https://www.math.stonybrook.edu/~kirillov/liegroups},
}

@book{lie-groups-serganova-student,
  title =     {261A Lie Groups},
  author =    {Yuan, Qiaochu},
  year =      {2013},
  url =       {https://math.berkeley.edu/~qchu/Notes/261A.pdf},
}

@book{humphreys,
  title =     {Introduction to Lie Algebras and Representation Theory},
  author =    {E. Humphreys, James},
  publisher = {Springer},
  year =      {1973},
  series =    {Graduate Texts in Mathematics},
  edition =   {1},
}

@book{humphreys-cat-o,
  title =     {Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$},
  author =    {E. Humphreys, James},
  publisher = {American Mathematical Society},
  year =      {2008},
  series =    {Graduate Studies in Mathematics},
  volume =    94,
}

@inproceedings{cohomologies-lie,
  booktitle = {Lie Groups and Lie Algebras II},
  title =     {Cohomologies of Lie Groups and Lie Algebras},
  author =    {L. Feigin, Boris and B. Fuchs, Dmitry},
  publisher = {Springer},
  series =    {Encyclopedia of Mathematics},
  volume =    21,
  year =      {2000},
}

@book{harder,
  title =     {Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces},
  author =    {Harder, G{\"u}nter},
  year =      {2008},
  publisher = {Springer}
}

@book{ribeiro,
  title =     {Notes of Everything},
  author =    {Ribeiro, Gabriel},
  year =      {2022},
  url =       {https://perso.pages.math.cnrs.fr/users/gabriel.ribeiro/assets/files/main.pdf}
}

@book{symplectic-physics,
  title =     {Symplectic Techniques in Physics},
  author =    {Guillemin, Victor and Sternberg, Shlomo},
  publisher = {Cambridge University Press},
  year =      {1984},
  edition =   {First Edition},
}

@book{goodearl-warfield,
  title =     {An Introduction to Noncommutative Noetherian Rings},
  author =    {R. Goodearl, Kenneth and Warfield Jr, Robert B.},
  publisher = {Cambridge University Press},
  year =      {2004},
  series =    {London Mathematical Society Student Texts},
  edition =   {Second Edition},
}

@misc{dimitar-exp,
  doi =       {10.48550/ARXIV.2011.09975},
  author =    {Grantcharov, Dimitar and Nguyen, Khoa},
  title =     {Exponentiation and Fourier transform of tensor modules of $\mathfrak { sl} (n+1)$},
  publisher = {arXiv},
  year =      {2020},
  copyright = {Creative Commons Zero v1.0 Universal}
}

@article{nilsson,
  title =     {$\mathcal{U}(\mathfrak{h})$-free modules and coherent families},
  journal =   {Journal of Pure and Applied Algebra},
  author =    {Nilsson, Jonathan},
  volume =    {220},
  number =    {4},
  pages =     {1475-1488},
  year =      {2016},
  doi =       {10.1016/j.jpaa.2015.09.013},
}

@article{fernando,
  title =     {Lie algebra modules with finite-dimensional weight spaces. I},
  author =    {Rupasiri Lakshman Fernando},
  journal =   {Transactions of the American Mathematical Society},
  doi =       {10.1090/S0002-9947-1990-1013330-8},
  year =      {1990},
  volume =    {322},
  pages =     {757-781},
}

@article{mathieu,
  author =    {Mathieu, Olivier},
  journal =   {Annales de l'institut Fourier},
  doi =       {10.5802/aif.1765},
  number =    {2},
  pages =     {537-592},
  publisher = {Association des Annales de l'Institut Fourier},
  title =     {Classification of irreducible weight modules},
  volume =    {50},
  year =      {2000},
}

@book{demazure-gabriel,
  title =     {Groupes Algebriques Tome 1},
  author =    {Demazure, Michel and Gabriel, Pierre},
  publisher = {NH},
  year =      {1970},
}

@book{coutinho,
  title =     {A Primer of Algebraic $D$-modules},
  author =    {C. Coutinho, Severino},
  publisher = {Cambridge University Press},
  year =      {1995},
  series =    {London Mathematical Society student texts 33},
}

@article{frobenius,
  title =     {{\"U}ber Gruppencharakteren},
  author =    {Frobenius, Ferdinand Georg},
  journal =   {Wiss. Berlin},
  pages =     {985--1021},
  year =      {1896}
}

@book{maclane,
   title =     {Categories for the Working Mathematician},
   author =    {Mac Lane, Saunders},
   publisher = {Springer-Verlag},
   year =      {1971},
   edition =   {6},
}