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
references.bib (5169B)

  1 @book{serganova,
  2   title =     {A Journey Through Representation Theory: From Finite Groups to Quivers via Algebras},
  3   author =    {Gruson, Caroline and Serganova, Vera},
  4   year =      {2018},
  5 }
  6 
  7 @book{fulton-harris,
  8   title =     {Representation Theory: A First Course},
  9   author =    {Fulton, William and Harris, Joe},
 10   publisher = {Springer},
 11   year =      {1991},
 12   series =    {Graduate Texts in Mathematics / Readings in Mathematics},
 13   edition =   {Corrected},
 14 }
 15 
 16 @book{etingof,
 17   title =     {Introduction to Representation Theory},
 18   author =    {Etingof, Pavel and Golberg, Oleg and Hensel, Sebastian and Liu, Tiankai and Schwendner, Alex  and Vaintrob, Dmitry and Yudovina, Elena},
 19   publisher = {American Mathematical Society},
 20   year =      {2011},
 21   series =    {Student Mathematical Library},
 22 }
 23 
 24 @book{kirillov,
 25   title =     {Introduction to Lie Groups and Lie Algebras},
 26   author =    {Kirillov, Alexander},
 27   edition =   {Preliminary version},
 28   year =      {2008},
 29   url =       {https://www.math.stonybrook.edu/~kirillov/liegroups},
 30 }
 31 
 32 @book{lie-groups-serganova-student,
 33   title =     {261A Lie Groups},
 34   author =    {Yuan, Qiaochu},
 35   year =      {2013},
 36   url =       {https://math.berkeley.edu/~qchu/Notes/261A.pdf},
 37 }
 38 
 39 @book{humphreys,
 40   title =     {Introduction to Lie Algebras and Representation Theory},
 41   author =    {E. Humphreys, James},
 42   publisher = {Springer},
 43   year =      {1973},
 44   series =    {Graduate Texts in Mathematics},
 45   edition =   {1},
 46 }
 47 
 48 @book{humphreys-cat-o,
 49   title =     {Representations of Semisimple Lie Algebras in the BGG Category $\mathcal{O}$},
 50   author =    {E. Humphreys, James},
 51   publisher = {American Mathematical Society},
 52   year =      {2008},
 53   series =    {Graduate Studies in Mathematics},
 54   volume =    94,
 55 }
 56 
 57 @inproceedings{cohomologies-lie,
 58   booktitle = {Lie Groups and Lie Algebras II},
 59   title =     {Cohomologies of Lie Groups and Lie Algebras},
 60   author =    {L. Feigin, Boris and B. Fuchs, Dmitry},
 61   publisher = {Springer},
 62   series =    {Encyclopedia of Mathematics},
 63   volume =    21,
 64   year =      {2000},
 65 }
 66 
 67 @book{harder,
 68   title =     {Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces},
 69   author =    {Harder, G{\"u}nter},
 70   year =      {2008},
 71   publisher = {Springer}
 72 }
 73 
 74 @book{ribeiro,
 75   title =     {Notes of Everything},
 76   author =    {Ribeiro, Gabriel},
 77   year =      {2022},
 78   url =       {https://perso.pages.math.cnrs.fr/users/gabriel.ribeiro/assets/files/main.pdf}
 79 }
 80 
 81 @book{symplectic-physics,
 82   title =     {Symplectic Techniques in Physics},
 83   author =    {Guillemin, Victor and Sternberg, Shlomo},
 84   publisher = {Cambridge University Press},
 85   year =      {1984},
 86   edition =   {First Edition},
 87 }
 88 
 89 @book{goodearl-warfield,
 90   title =     {An Introduction to Noncommutative Noetherian Rings},
 91   author =    {R. Goodearl, Kenneth and Warfield Jr, Robert B.},
 92   publisher = {Cambridge University Press},
 93   year =      {2004},
 94   series =    {London Mathematical Society Student Texts},
 95   edition =   {Second Edition},
 96 }
 97 
 98 @misc{dimitar-exp,
 99   doi =       {10.48550/ARXIV.2011.09975},
100   author =    {Grantcharov, Dimitar and Nguyen, Khoa},
101   title =     {Exponentiation and Fourier transform of tensor modules of $\mathfrak { sl} (n+1)$},
102   publisher = {arXiv},
103   year =      {2020},
104   copyright = {Creative Commons Zero v1.0 Universal}
105 }
106 
107 @article{nilsson,
108   title =     {$\mathcal{U}(\mathfrak{h})$-free modules and coherent families},
109   journal =   {Journal of Pure and Applied Algebra},
110   author =    {Nilsson, Jonathan},
111   volume =    {220},
112   number =    {4},
113   pages =     {1475-1488},
114   year =      {2016},
115   doi =       {10.1016/j.jpaa.2015.09.013},
116 }
117 
118 @article{fernando,
119   title =     {Lie algebra modules with finite-dimensional weight spaces. I},
120   author =    {Rupasiri Lakshman Fernando},
121   journal =   {Transactions of the American Mathematical Society},
122   doi =       {10.1090/S0002-9947-1990-1013330-8},
123   year =      {1990},
124   volume =    {322},
125   pages =     {757-781},
126 }
127 
128 @article{mathieu,
129   author =    {Mathieu, Olivier},
130   journal =   {Annales de l'institut Fourier},
131   doi =       {10.5802/aif.1765},
132   number =    {2},
133   pages =     {537-592},
134   publisher = {Association des Annales de l'Institut Fourier},
135   title =     {Classification of irreducible weight modules},
136   volume =    {50},
137   year =      {2000},
138 }
139 
140 @book{demazure-gabriel,
141   title =     {Groupes Algebriques Tome 1},
142   author =    {Demazure, Michel and Gabriel, Pierre},
143   publisher = {NH},
144   year =      {1970},
145 }
146 
147 @book{coutinho,
148   title =     {A Primer of Algebraic $D$-modules},
149   author =    {C. Coutinho, Severino},
150   publisher = {Cambridge University Press},
151   year =      {1995},
152   series =    {London Mathematical Society student texts 33},
153 }
154 
155 @article{frobenius,
156   title =     {{\"U}ber Gruppencharakteren},
157   author =    {Frobenius, Ferdinand Georg},
158   journal =   {Wiss. Berlin},
159   pages =     {985--1021},
160   year =      {1896}
161 }
162 
163 @book{maclane,
164    title =     {Categories for the Working Mathematician},
165    author =    {Mac Lane, Saunders},
166    publisher = {Springer-Verlag},
167    year =      {1971},
168    edition =   {6},
169 }