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1

A, Lohe M., ed. Quantum group symmetry and q-tensor algebras. Singapore: World Scientific, 1995.

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2

Iwahori-Hecke algebras and Schur algebras of the symmetric group. Providence, R.I: American Mathematical Society, 1999.

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3

Linear and projective representations of symmetric groups. Cambridge, U.K: Cambridge University Press, 2005.

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4

Symmetric and G-algebras: With applications to group representations. Dordrecht: Kluwer Academic Publishers, 1990.

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5

R, Wallach Nolan, ed. Symmetry, representations, and invariants. Dordrecht [Netherlands]: Springer, 2009.

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6

Symmetries. [London]: Springer, 2001.

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7

Fabio, Scarabotti, and Tolli Filippo 1968-, eds. Representation theory of the symmetric groups: The Okounkov-Vershik approach, character formulas, and partition algebras. New York: Cambridge University Press, 2010.

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8

Kerber, Adalbert. Algebraic combinatorics via finite group actions. Mannheim: B.I. Wissenschaftsverlag, 1991.

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9

Evans, David E. Quantum symmetries on operator algebras. Oxford: Clarendon Press, 1998.

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10

Bernhard, Leeb, and Millson John J. 1946-, eds. The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra. Providence, R.I: American Mathematical Society, 2008.

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11

Kapovich, Michael. The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra. Providence, R.I: American Mathematical Society, 2008.

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12

Goldschmidt, David M. Group characters, symmetric functions, and the Hecke algebras. Providence, R.I: American Mathematical Society, 1993.

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13

Smooth compactifications of locally symmetric varieties. 2nd ed. Cambridge, UK: Cambridge University Press, 2010.

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14

I︠A︡glom, I. M. Geometries, groups and algebras in the nineteenth century: A history. Bronx, NY: ISHI Press, Inc., 2009.

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15

Abubakar, Ahmed Bello. The structure of symmetric group algebras at arbitrary characteristic. London: University of East London, 1999.

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16

Goldschmidt, David M. Group characters, symmetric functions, and the Hecke algebra. Providence, R.I: American Mathematical Society, 1993.

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17

1974-, Mahajan Swapneel Arvind, ed. Monoidal functors, species, and Hopf algebras. Providence, R.I: American Mathematical Society, 2010.

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18

Quantum bounded symmetric domains. Providence, R.I: American Mathematical Society, 2010.

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19

Bratteli, Ola. Operator Algebras and Quantum Statistical Mechanics 1: C*- and W*-Algebras Symmetry Groups Decomposition of States. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987.

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20

Vladimir, Shchigolev, ed. Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n). Providence, Rhode Island: American Mathematical Society, 2012.

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21

1948-, Erdmann Karin, and Schocker Manfred, eds. Polynomial representations of GLn. 2nd ed. New York: Springer, 2006.

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22

Green, J. A. Polynomial representations of GLn. 2nd ed. Berlin: Springer, 2007.

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23

Gurahick, Robert M. Symmetric and alternating groups as monodromy groups of Riemann surfaces I: Generic covers and covers with many branch points. Providence, RI: American Mathematical Society, 2007.

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24

Symmetrie, Gruppe, Dualität: Zur Beziehung zwischen theoretischer Mathematik und Anwendungen in Kristallographie und Baustatik des 19. Jahrhunderts. Basel: Birkhäuser Basel, 1989.

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25

Jürgen, Fuchs. Symmetries, lie algebras and representations: A graduate course for physicists. Cambridge: Cambridge University Press, 2003.

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26

Jürgen, Fuchs. Symmetries, lie algebras and representations: A graduate course for physicists. Cambridge, U.K: Cambridge University Press, 1997.

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27

Tensor categories. Providence, Rhode Island: American Mathematical Society, 2015.

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28

Differential geometry, Lie groups, and symmetric spaces over general base fields and rings. Providence, R.I: American Mathematical Society, 2008.

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29

1980-, Blazquez-Sanz David, Morales Ruiz, Juan J. (Juan José), 1953-, and Lombardero Jesus Rodriguez 1961-, eds. Symmetries and related topics in differential and difference equations: Jairo Charris Seminar 2009, Escuela de Matematicas, Universidad Sergio Arboleda, Bogotá, Colombia. Providence, R.I: American Mathematical Society, 2011.

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30

Extended graphical calculus for categorified quantum sl(2). Providence, R.I: American Mathematical Society, 2011.

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31

Etingof, P. I. Lectures on representation theory and Knizhnik-Zamolodchikov equations. Providence, R.I: American Mathematical Society, 1998.

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32

Espaces symétriques de Drinfeld. Paris: Société mathématique de France, 1996.

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33

Genestier, Alain. Espaces symétriques de Drinfeld. Paris: Société mathématique de France, 1996.

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34

Genestier, Alain. Espaces symétriques de Drinfeld. Paris: Société Mathématique de France, 1996.

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35

Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.

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36

Manivel, Laurent. Fonctions symétriques, polynômes de Schubert et lieux de dégénérescence. Paris: Société Mathématique de France, 1998.

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37

Bárcenas, Noé, and Monica Moreno Rocha. Mexican mathematicians abroad: Recent contributions : first workshop, Matematicos Mexicanos Jovenes en el Mundo, August 22-24, 2012, Centro de Investigacion en Matematicas, A.C., Guanajuato, Mexico. Edited by Galaz-García Fernando editor. Providence, Rhode Island: American Mathematical Society, 2016.

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38

Conference on Hopf Algebras and Tensor Categories (2011 University of Almeria). Hopf algebras and tensor categories: International conference, July 4-8, 2011, University of Almería, Almería, Spain. Edited by Andruskiewitsch Nicolás 1958-, Cuadra Juan 1975-, and Torrecillas B. (Blas) 1958-. Providence, Rhode Island: American Mathematical Society, 2013.

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39

Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

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40

Roe, John. Winding around: The winding number in topology, geometry, and analysis. Providence, Rhode Island: American Mathematical Society, 2015.

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41

I, Arnolʹd V. Experimental mathematics. Berkeley, California: MSRI Mathematical Sciences Research Institute, 2015.

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42

Biedenharn, L. C., and M. A. Lohe. Quantum Group Symmetry and Q-Tensor Algebras. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/2815.

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43

Representations of the Infinite Symmetric Group. Cambridge University Press, 2016.

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44

Noncommutative Character Theory Of The Symmetric Group. Imperial College Press, 2005.

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45

Symmetries in Science Vi: From The Rotation Group To Quantum Algebras. Springer, 2013.

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46

1936-, Gruber Bruno, ed. Symmetries in science VI: From the rotation group to quantum algebras. New York: Plenum Press, 1994.

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47

Singer, Stephanie Frank Frank. Linearity, Symmetry, and Prediction in the Hydrogen Atom. Springer, 2010.

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48

Ceulemans, Arnout, and Pieter Thyssen. Shattered Symmetry: Group Theory from the Eightfold Way to the Periodic Table. Oxford University Press, Incorporated, 2017.

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49

Gruber, Samuel H. Symmetries in Science VI: From the Rotation Group to Quantum Algebras (Symmetries in Science). Springer, 1993.

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50

Ortaçgil, Ercüment H. The Symmetry Group. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821656.003.0016.

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This chapter, which ends Part II on some consequences of the new approach, introduces an alternative prolongation theory of Klein geometries that is more geometric and intuitive than the well-known prolongation theory of a linear Lie algebra developed by Guillemin, Singer, and Sternberg.
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