============
Bibliography
============

.. [BumpNakasuji2010] D. Bump and M. Nakasuji. Casselman's basis of
   Iwahori vectors and the Bruhat order. arXiv:1002.2996,
   http://arxiv.org/abs/1002.2996.

.. [Carrell1994] J. B. Carrell. The Bruhat graph of a Coxeter group, a
   conjecture of Deodhar, and rational smoothness of Schubert varieties. In
   *Algebraic Groups and Their Generalizations: Classical Methods*,
   AMS Proceedings of Symposia in Pure Mathematics, 56, 53--61, 1994.

.. [Deodhar1977] V. V. Deodhar. Some characterizations of Bruhat
   ordering on a Coxeter group and determination of the relative
   Moebius function. Inventiones Mathematicae, 39(2):187--198, 1977.

.. [Dyer1993] M. J. Dyer. The nil Hecke ring and Deodhar's conjecture
   on Bruhat intervals. Inventiones Mathematicae, 111(1):571--574, 1993.

.. [Dynkin1952] E. B. Dynkin,
   Semisimple subalgebras of semisimple Lie algebras. (Russian) 
   Mat. Sbornik N.S. 30(72):349–462, 1952.

.. [FauserEtAl2006] B. Fauser, P. D. Jarvis, R. C. King, and
   B. G. Wybourne. New branching rules induced by plethysm. *Journal of
   Physics A*. 39(11):2611--2655, 2006.

.. [Fulton1997] W. Fulton. *Young Tableaux*. Cambridge University
   Press, 1997.

.. [FourierEtAl2009] G. Fourier, M. Okado, A. Schilling.
   Kirillov--Reshetikhin crystal for nonexceptional types.
   *Advances in Mathematics*, 222:1080--1116, 2009.

.. [FourierEtAl2010] G. Fourier, M. Okado, A. Schilling.
   Perfectness of Kirillov-Reshetikhin crystals for nonexceptional types.
   *Contemp. Math.*, 506:127--143, 2010.

.. [HatayamaEtAl2001] G. Hatayama, A. Kuniba, M. Okado, T. Takagi, Z. Tsuboi.
   Paths, crystals and fermionic formulae.
   in MathPhys Odyssey 2001, in : Prog. Math. Phys., vol 23, Birkhauser Boston, Boston, MA 2002,
   pp. 205--272.

.. [HainesEtAl2009] T. J. Haines, R. E. Kottwitz, and
   A. Prasad. Iwahori-Hecke Algebras. arXiv:math/0309168,
   http://arxiv.org/abs/math/0309168.

.. [HongKang2002] J. Hong and S.-J. Kang. *Introduction to Quantum
   Groups and Crystal Bases*. AMS Graduate Studies in Mathematics,
   American Mathematical Society, 2002.

.. [HoweEtAl2005] R. Howe, E.-C.Tan, and J. F. Willenbring. Stable
   branching rules for classical symmetric pairs. *Transactions of the
   American Mathematical Society*, 357(4):1601--1626, 2005.

.. [Iwahori1964] N. Iwahori. On the structure of a Hecke ring of a
   Chevalley group over a finite field. *J. Fac. Sci. Univ. Tokyo
   Sect. I*, 10:215--236, 1964.

.. [Jimbo1986] M. A. Jimbo. `q`-analogue of `U(\mathfrak{gl}(N+1))`,
   Hecke algebra, and the Yang-Baxter equation.
   *Lett. Math. Phys*, 11(3):247--252, 1986.

.. [JonesEtAl2010] B. Jones, A. Schilling.
   Affine structures and a tableau model for E_6 crystals
   *J. Algebra*, 324:2512-2542, 2010

.. [Kashiwara1995] M. Kashiwara. On crystal bases. Representations of
   groups (Banff, AB, 1994), 155--197, CMS Conference Proceedings, 16,
   American Mathematical Society, Providence, RI, 1995.

.. [KashiwaraNakashima1994] M. Kashiwara and T. Nakashima. Crystal
   graphs for representations of the `q`-analogue of classical Lie
   algebras. *Journal Algebra*, 165(2):295--345, 1994.

.. [King1975] R. C. King. Branching rules for classical Lie groups
   using tensor and spinor methods. *Journal of Physics A*,
   8:429--449, 1975.

.. [Knuth1970] D. Knuth. Permutations, matrices, and generalized Young
   tableaux. *Pacific Journal of Mathematics*, 34(3):709--727, 1970.

.. [Knuth1998] D. Knuth. *The Art of Computer
   Programming. Volume 3. Sorting and Searching*. Addison Wesley
   Longman, 1998.

.. [KKMMNN1992] S-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa,
   T. Nakashima, A. Nakayashiki.
   Affine crystals and vertex models.
   *Int. J. Mod. Phys.* A 7 (suppl. 1A): 449--484, 1992.

.. [McKayPatera1981] W. G. McKay and J. Patera. *Tables of Dimensions,
   Indices and Branching Rules for Representations of Simple Lie
   Algebras*. Marcel Dekker, 1981.

.. [OkadoSchilling2008] M. Okado, A.Schilling. Existence of crystal bases for
   Kirillov--Reshetikhin crystals for nonexceptional types.
   *Representation Theory* 12:186--207, 2008.

.. [Seitz1991] G. Seitz,
   Maximal subgroups of exceptional algebraic groups. 
   Mem. Amer. Math. Soc. 90 (1991), no. 441.

.. [Rubenthaler2008] H. Rubenthaler, 
   The (A2,G2) duality in E6, octonions and the triality principle.
   Trans. Amer. Math. Soc. 360 (2008), no. 1, 347–367 

.. [SchillingTingley2011] A. Schilling, P. Tingley.
   Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function.
   preprint arXiv:1104.2359

.. [Stanley1999] R. P. Stanley. *Enumerative Combinatorics, Volume
   2*. Cambridge University Press, 1999.

.. [Testerman1989] Testerman, Donna M.
   A construction of certain maximal subgroups of the algebraic groups E6 and F4. 
   J. Algebra 122 (1989), no. 2, 299–322. 

.. [Testerman1992] Testerman, Donna M. The construction of the maximal A1's in
   the exceptional algebraic groups. Proc. Amer. Math. Soc. 116 (1992), no. 3, 635–644.