Automorphism Groups of Strong Bruhat Orders of Coxeter Groups

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In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedral ... continued below

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iv, 76 leaves: ill.

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Sutherland, David C. (David Craig) August 1986.

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  • Sutherland, David C. (David Craig)

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Description

In this dissertation, we describe the automorphism groups for the strong Bruhat orders A_n-1, B_n, and D_n. In particular, the automorphism group of A_n-1 for n ≥ 3 is isomorphic to the dihedral group of order eight, D_4; the automorphism group of B_n for n ≥ 3 is isomorphic to C_2 x C_2 where C_2 is the cyclic group of order two; the automorphism group of D_n for n > 5 and n even is isomorphic to C_2 x C_2 x C_2; and the automorphism group of D_n for n ≥ 5 and n odd is isomorphic to the dihedral group D_4.

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iv, 76 leaves: ill.

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  • August 1986

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  • Aug. 22, 2014, 6 p.m.

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  • April 12, 2016, 10:29 a.m.

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Sutherland, David C. (David Craig). Automorphism Groups of Strong Bruhat Orders of Coxeter Groups, dissertation, August 1986; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc330906/: accessed October 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .