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Parabolic double cosets in Coxeter groups [Elektronski vir]Billey, Sara C. ...Parabolične podrupe ▫$W_I$▫ Coxeterjevega sistema ▫$(W,S)$▫, tako kot tudi njihove običajni in dvojni odseki ▫$W / W_I$▫ in ▫$W_I \setminus W / W_J$▫, se pojavljajo v mnogo kontekstih v kombinatoriki ... in Liejevi teoriji, vključno z geometrijo in topologijo posplošene praporne varietete in grupami simetrij pravilnih politopov. Množica običajnih odsekov ▫$w W_I$▫ za ▫$I \subseteq S$▫ tvori Coxeterjev komplekst grupe ▫$W$▫ in je dobro znana. V tem članku si ogledamo manj študiran objekt: množico dvojnih odsekov ▫$W_I w W_J$▫ za ▫$I, J \subseteq S$▫. Vsak dvojni odsek je lahko predstavljen z mnogimi različnimi trojicami ▫$(I,w,J)$▫. Opišemo leksikografsko minimalno prezentacijo in dokažemo, da je za vsak dvojni odsek taka prezentacija enolična. Leksikografsko minimalne prezentacije lahko preštejemo preko končnega avtomata, odvisnega od Coxeterjevega grafa za ▫$(W,S)$▫. V posebnem predstavimo formulo za število paraboličnih dvojnih odsekov s fiksnim minimalnim elementom, ko je ▫$W$▫ simetrična grupa ▫$S_n$▫. V tem primeru paraboličnim podgrupam rečemo tudi Youngove podgrupe. Naša formula je skoraj vedno izračunljiva v času, linearnem v ▫$n$▫, in se lahko posploši na poljubno Coxeterjevo grupo. Pokažemo tudi formule za vse končne in afine Weylove grupe, ko je ▫$w$▫ identiteta.Source: The Electronic journal of combinatorics [Elektronski vir]. - ISSN 1077-8926 (Vol. 25, iss. 1, 2018, paper P1.23 (66 str.))Type of material - e-articlePublish date - 2018Language - englishCOBISS.SI-ID - 18573145
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Database name | Field | Year |
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Billey, Sara C. | ![]() |
Konvalinka, Matjaž | 22401 |
Petersen, T. Kyle | ![]() |
Slofstra, William | ![]() |
Tenner, Bridget E. | ![]() |
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