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1

Nomizu, Katsumi. Affine differential geometry: Geometry of affine immersions. Cambridge: Cambridge University Press, 1994.

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2

Bergmann, Artur, and Erich Baumgartner. Affine Ebenen. München: Oldenbourg Wissenschaftsverlag Verlag, 2013. http://dx.doi.org/10.1524/9783486747102.

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3

Snapper, Ernst. Metric affine geometry. New York: Dover Publications, 1989.

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4

Gutierrez, Jaime, Vladimir Shpilrain, and Jie-Tai Yu, eds. Affine Algebraic Geometry. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/conm/369.

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5

Gao, Yun, Naihuan Jing, Michael Lau, and Kailash C. Misra, eds. Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/conm/506.

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6

Bennett, M. K. Affine and Projective Geometry. Hoboken, NJ, USA: John Wiley & Sons, Inc., 1995. http://dx.doi.org/10.1002/9781118032565.

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7

van den Essen, Arno, ed. Automorphisms of Affine Spaces. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8555-2.

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8

Shapiro, Larry S. Affine analysis of image sequences. New York: Cambridge University Press, 1995.

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9

Bobadilla, Javier Fernández de. Moduli spaces of polynomials in two variables. Providence, R.I: American Mathematical Society, 2005.

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10

Russell, P., Daniel Daigle, Richard Ganong, and Mariusz Koras. Affine algebraic geometry: The Russell festschrift. Providence, R.I: American Mathematical Society, 2011.

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11

Xi, Nanhua. Representations of affine Hecke algebras. Berlin: Springer-Verlag, 1994.

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12

Xi, Nanhua. Representations of Affine Hecke Algebras. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074130.

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13

Adamović, Dražen, and Paolo Papi, eds. Affine, Vertex and W-algebras. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-32906-8.

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14

Leichtweiss, K. Affine geometry of convex bodies. Heidelberg: Barth, 1998.

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15

Backus, David. Affine models of currency pricing. Cambridge, MA: National Bureau of Economic Research, 1996.

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16

Futorny, V. Representations of affine Lie algebras. Kingston, Ont: Queen's University, 1997.

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17

1963-, Gao Yun, ed. Quantum affine algebras, extended affine Lie algebras, and their applications: Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, March 2-7, 2008, Banff International Research Station, Banff, Canada. Providence, R.I: American Mathematical Society, 2010.

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18

Dai, Qiang. Specification analysis of affine term structure models. Cambridge, MA: National Bureau of Economic Research, 1997.

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19

Tecklenburg, H. Stufen der Anordnung in Geometrie und Algebra. Wiesbaden: Deutscher Universitäts-Verlag, 1992.

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20

Goldblatt, Robert. Orthogonality and spacetime geometry. New York: Springer-Verlag, 1987.

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21

Workshop on Quantum Affine Lie Algebras, Extended Affine Lie algebras, and Applications (2008 Banff International Research Station). Quantum affine algebras, extended affine Lie algebras, and their applications: Workshop on Quantum Affine Lie Algebras, Extended Affine Lie algebras, and Applications, March 2-7, 2008, Banff International Research Station, Banff, Canada. Edited by Gao Yun 1963-. Providence, R.I: American Mathematical Society, 2010.

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22

García-Río, Eduardo, Peter Gilkey, Stana Nikčević, and Ramón Vázquez-Lorenzo. Applications of Affine and Weyl Geometry. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-031-02405-4.

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23

Kuroda, Shigeru, Nobuharu Onoda, and Gene Freudenburg, eds. Polynomial Rings and Affine Algebraic Geometry. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42136-6.

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24

Cheltsov, Ivan, Ciro Ciliberto, Hubert Flenner, James McKernan, Yuri G. Prokhorov, and Mikhail Zaidenberg, eds. Automorphisms in Birational and Affine Geometry. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05681-4.

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25

Reventós Tarrida, Agustí. Affine Maps, Euclidean Motions and Quadrics. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-710-5.

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26

Schmitt, Alexander, ed. Affine Flag Manifolds and Principal Bundles. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0288-4.

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27

Kao, Chang-Lung. Affine invariant matching of noisy objects. Monterey, Calif: Naval Postgraduate School, 1989.

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28

Fu, Xiaoye. Self-affine scaling sets in R². Providence, Rhode Island: American Mathematical Society, 2014.

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29

Ma, S. K. Tracking corner features using affine transformations. Manchester: UMIST, 1997.

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30

Martin, Wiehe, Simon Udo 1938-, Opozda Barbara, and Stefan Banach International Mathematical Center., eds. PDEs, submanifolds, and affine differential geometry. Warszawa: Polish Academy of Sciences, Institute of Mathematics, 2002.

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31

Lamdan, Yehezkel. Object recognition by affine invariant matching. New York: Courant Institute of Mathematical Sciences, New York University, 1988.

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32

Northcott, D. G. Affine Sets and Affine Groups. Cambridge University Press, 2013.

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33

Northcott, D. G. Affine Sets and Affine Groups. Cambridge University Press, 2013.

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34

Salkowski, Erich. Affine Differentialgeometrie. De Gruyter, Inc., 2020.

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35

Ball, Kimber Lee. April Affine. PANN Publishing Company, 2016.

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36

Nomizu, Katsumi, and Takeshi Sasaki. Affine Differential Geometry: Geometry of Affine Immersions. Cambridge University Press, 2008.

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37

Troyer, Robert J., and Ernst Snapper. Metric Affine Geometry. Elsevier Science & Technology Books, 2014.

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38

Gurjar, Rajendra V., Kayo Masuda, and Masayoshi Miyanishi. Affine Space Fibrations. De Gruyter, 2021. http://dx.doi.org/10.1515/9783110577563.

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39

Bennett, Curtis D. Affine [lambda]-buildings. 1990.

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40

Affine Algebraic Geometry. World Scientific Publishing Co Pte Ltd, 2013.

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41

Miyanishi, Masayoshi, Kayo Masuda, and Rajendra V. Gurjar. Affine Space Fibrations. de Gruyter GmbH, Walter, 2021.

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42

Miyanishi, Masayoshi, Kayo Masuda, and Rajendra V. Gurjar. Affine Space Fibrations. de Gruyter GmbH, Walter, 2021.

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43

Miyanishi, Masayoshi, Kayo Masuda, and Rajendra V. Gurjar. Affine Space Fibrations. de Gruyter GmbH, Walter, 2021.

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44

Zürich, Eidgenössische Technische Hochschule, ed. Affine invariant regions ++. 2004.

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45

Affine insertion and Pieri rules for the affine Grassmannian. Providence, R.I: American Mathematical Society, 2010.

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46

Submanifolds of Affine Spaces: An Introduction to Affine Differential Geometry. World Scientific Pub Co Inc, 2007.

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47

Takeshi, Sasaki, and Katsumi Nomizu. Affine Differential Geometry: Geometry of Affine Immersions (Cambridge Tracts in Mathematics). Cambridge University Press, 1995.

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48

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Affine Fixed Point Buildings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0027.

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This chapter shows that if Ξ‎ is an affine building and Γ‎ is a finite descent group of Ξ‎, then Γ‎ is a descent group of Ξ‎∞ and (Ξ‎∞) is congruent to (Ξ‎∞). Ξ‎Γ‎ and Ξ‎ can be viewed as metric spaces. The chapter first considers the assumptions that Π‎ is an irreducible affine Coxeter diagram, Ξ‎ is a thick building of type Ξ‎, Γ‎is a finite descent group of Ξ‎, and Tits index �� = (Π‎, Θ‎, A). It then describes apartments that are endowed with reflection hyperplanes and reflection half-spaces before concluding with a theorem about a canonical isomorphism from the fixed point building Ξ‎Γ‎ to (Ξ‎Γ‎).
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49

Bennett, M. K. Affine and Projective Geometry. Wiley & Sons, Incorporated, John, 2011.

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50

Affine and Projective Geometry. Wiley & Sons Canada, Limited, John, 2011.

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