Shadows in the Wild - Folded Galleries and Their Applications

Abramenko, P., Brown, K.S.: Theory and applications. In: Buildings. Graduate Texts in Mathematics, vol. 248. Springer, New York (2008)

Berenstein, A., Kapovich, M.: Affine buildings for dihedral groups. Geom. Dedicata 156, 171–207 (2012)

Björner, A., Brenti, F.: Combinatorics of Coxeter Groups. Graduate Texts in Mathematics, vol. 231. Springer, New York (2005)

Bourbaki, N.: Elements of Mathematics. Lie Groups and Lie Algebras. Springer, Berlin (2008), Chapters 4–6

Braverman, A., Gaitsgory, D.: Crystals via the affine Grassmannian. Duke Math. J. 107(3), 561–575 (2001)

Brewster Lewis, J., McCammond, J., Kyle Petersen, T., Schwer, P.: Computing reflection length in an affine Coxeter group. Trans. Am. Math. Soc. 371(6), 4097–4127 (2019)

Bridson, M.R., Haefliger, A.: Metric Spaces of Non-positive Curvature. Grundlehren der Mathematischen Wissenschaften, vol. 319. Springer, Berlin (1999)

Brown, K.S.: Buildings. Springer, New York (1989)

Davis, M.W.: The Geometry and Topology of Coxeter Groups. London Mathematical Society Monographs Series, vol. 32. Princeton University Press, Princeton (2008)

Davis, M.W.: Examples of buildings constructed via covering spaces. Groups Geom. Dyn. 3(2), 279–298 (2009)

Deligne, P., Lusztig, G.: Representations of reductive groups over finite fields. Ann. of Math. (2) 103(1), 103–161 (1976)

Deodhar, V.V.: On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells. Invent. Math. 79(3), 499–511 (1985)

Funk, M., Strambach, K.: Free constructions. In: Handbook of Incidence Geometry, pp. 739–780. North-Holland, Amsterdam (1995)

Garrett, P.: Buildings and Classical Groups. Chapman & Hall, London (1997)

Gaussent, S., Littelmann, P.: LS galleries, the path model, and MV cycles. Duke Math. J. 127(1), 35–88 (2005)

Görtz, U., Haines, T.J., Kottwitz, R.E., Reuman, D.C.: Dimensions of some affine Deligne-Lusztig varieties. Ann. Sci. École Norm. Sup. (4) 39(3), 467–511 (2006)

Görtz, U., Haines, T.J., Kottwitz, R.E., Reuman, D.C.: Affine Deligne–Lusztig varieties in affine flag varieties. Compositio Mathematica 146(5), 1339–1382 (2010)

Görtz, U., He, X., Nie, S.: $\mathbf{P} $-alcoves and nonemptiness of affine Deligne-Lusztig varieties. Ann. Sci. Éc. Norm. Supér. (4) 48(3), 647–665 (2015)

Graeber, M., Schwer, P.: Shadows in Coxeter groups. Ann. Comb. 24(1), 119–147 (2020)

Griffeth, S., Ram, A.: Affine Hecke algebras and the Schubert calculus. European J. Combin. 25(8), 1263–1283 (2004)

He, X.: Note on affine Deligne-Lusztig varieties (2013). 1309.0075 [math.AG]

He, X.: Geometric and homological properties of affine Deligne-Lusztig varieties. Ann. of Math. (2) 179(1), 367–404 (2014)

He, X., Yu, Q.: Dimension formula for the affine Deligne-Lusztig variety $X(\mu , b)$. Math. Ann. 379(3–4), 1747–1765 (2021)

Hitzelberger, P.: Kostant convexity for affine buildings. Forum Math. 22(5), 959–971 (2010)

Hitzelberger, P.: Non-discrete affine buildings and convexity. Adv. Math. 227(1), 210–244 (2011)

Humphreys, J.E.: Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics, vol. 29. Cambridge University Press, Cambridge (1990)

Kamnitzer, J.: Mirković-Vilonen cycles and polytopes. Ann. of Math. (2) 171(1), 245–294 (2010)

Kapovich, M., Millson, J.J.: A path model for geodesics in Euclidean buildings and its applications to representation theory. Groups Geom. Dyn. 2(3), 405–480 (2008)

Kashiwara, M.: Crystalizing the q-analogue of universal enveloping algebras. Commun. Math. Phys. 133(2), 249–260 (1990)

Kostant, B.: On convexity, the Weyl group and the Iwasawa decomposition. Ann. Sci. Éc. Norm. Supér. 4(6), 413–455 (1973)

Lakshmibai, V., Seshadri, C.S.: Standard monomial theory. In: Proceedings of the Hyderabad Conference on Algebraic Groups, Hyderabad, 1989, pp. 279–322. Manoj Prakashan, Madras (1991)

Littelmann, P.: A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras. Invent. Math. 116(1–3), 329–346 (1994)

Littelmann, P.: Paths and root operators in representation theory. Ann. of Math. (2) 142(3), 499–525 (1995)

Lusztig, G.: Representations of Finite Chevalley Groups. CBMS Regional Conference Series in Mathematics, vol. 39, pp. 8–12. Am. Math. Soc., Providence (1978). Expository lectures from the CBMS Regional Conference held at, Madison, Wis, 1977

Lusztig, G.: Canonical bases arising from quantized enveloping algebras. J. Amer. Math. Soc. 3(2), 447–498 (1990)

Lusztig, G.: An algebraic-geometric parametrization of the canonical basis. Adv. Math. 120(1), 173–190 (1996)

Matsumoto, H.: Générateurs et relations des groupes de Weyl généralisés. C. R. Acad. Sci. Paris 258, 3419–3422 (1964)

Ehrig, M.: MV-polytopes via affine buildings. Duke Math. J. 155(3), 433–482 (2010)

Milićević, E., Schwer, P., Thomas, A.: Dimensions of Affine Deligne-Lusztig Varieties: A New Approach via Labeled Folded Alcove Walks and Root Operators. Mem. Amer. Math. Soc. vol. 261(1260), (2019), v+101

Milićević, E., Naqvi, Y., Schwer, P., Thomas, A.: A gallery model for affine flag varieties via chimney retractions, (2020). 1912.09911 [math.RT] 39 pages, 2020

Milićević, E., Schwer, P., Thomas, A.: Affine Deligne-Lusztig varieties and folded galleries governed by chimneys (2020). 2006.16288 [math.AG], 53 pages, 2020

Parkinson, J., Ram, A., Schwer, C.: Combinatorics in affine flag varieties. J. Algebra 321(11), 3469–3493 (2009)

Ram, A.: Alcove walks, Hecke algebras, spherical functions, crystals and column strict tableaux. Pure Appl. Math. Q., 2(4), 963–1013 (2006). Special Issue: In honor of Robert D. MacPherson. Part 2

Ram, A., Yip, M.: A combinatorial formula for Macdonald polynomials. Adv. Math. 226(1), 309–331 (2011)

Rapoport, M.: A positivity property of the Satake isomorphism. Manuscripta Math. 101(2), 153–166 (2000)

Ronan, M.: A construction of buildings with no rank 3 residues of spherical type. In: Buildings and the Geometry of Diagrams, Lect. 3rd 1984 Sess. C.I.M.E., Como/Italy, 1984. Lect. Notes Math., vol. 1181, pp. 242–248 (1986)

Ronan, M.: Construction and automorphisms of buildings. In: Essays in Geometric Group Theory. Ramanujan Math. Soc. Lect. Notes Ser., vol. 9, pp. 125–143. Ramanujan Math. Soc., Mysore (2009)

Ronan, M.: Lectures on Buildings. University of Chicago Press, Chicago (2009). Updated and revised

Ronan, M., Tits, J.: Building buildings. Math. Ann. 278, 291–306 (1987)

Schwer, C.: Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra. Int. Math. Res. Not. 2006, 75395 (2006)

Serre, J.-P.: Trees. Springer Monographs in Mathematics. Springer, Berlin (2003). Translated from the French original by John Stillwell, Corrected 2nd printing of the 1980 English translation

Tits, J.: Immeubles de type affine. (Buildings of affine type). In: Buildings and the Geometry of Diagrams, Lect. 3rd 1984 Sess. C.I.M.E., Como/Italy, 1984. Lect. Notes Math., vol. 1181, pp. 159–190 (1986)

Tits, J.: Groupes et Géométries de Coxeter. IHES Notes polycopies 1960 (1960)

Weiss, R.M.: The Structure of Affine Buildings. Annals of Mathematics Studies, vol. 168. Princeton University Press, Princeton (2009)

Zhu, X.: An introduction to affine Grassmannians and the geometric Satake equivalence. In: Geometry of Moduli Spaces and Representation Theory. Lecture Notes from the 2015 IAS/Park City Mathematics Institute, (PCMI) Graduate Summer School, Park City, UT, USA, June 28 – July 18, 2015, pp. 59–154. Institute for Advanced Study (IAS)/American Mathematical Society (AMS), Providence/Princeton (2017)