Buchumschlag

The geometry of conjugation in affine Coxeter groups

We develop precise geometric descriptions of the conjugacy class [x] and coconjugation set C(x,x')={y∈W̄|yxy−1=x'} for all elements x,x' of any affine Coxeter group W̄. The centralizer of x in ̄W is the special case C(x,x). The key structure in our description of the conjugacy class [...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Milićević, Elizabeth (VerfasserIn) , Schwer, Petra (VerfasserIn) , Thomas, Anne (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2025
In: International journal of algebra and computation
Year: 2025, Jahrgang: 35, Heft: 03, Pages: 403-465
ISSN:0218-1967
DOI:10.1142/S0218196725500109
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S0218196725500109
Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/10.1142/S0218196725500109
Volltext
Verfasserangaben:Elizabeth Milićević, Petra Schwer, and Anne Thomas

MARC

LEADER 00000naa a2200000 c 4500
001 1937633896
003 DE-627
005 20251002120728.0
007 cr uuu---uuuuu
008 251002s2025 xx |||||o 00| ||eng c
024 7 |a 10.1142/S0218196725500109  |2 doi 
035 |a (DE-627)1937633896 
035 |a (DE-599)KXP1937633896 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 27  |2 sdnb 
100 1 |a Milićević, Elizabeth  |e VerfasserIn  |0 (DE-588)1201613906  |0 (DE-627)1685691773  |4 aut 
245 1 4 |a The geometry of conjugation in affine Coxeter groups  |c Elizabeth Milićević, Petra Schwer, and Anne Thomas 
264 1 |c 2025 
300 |a 63 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a Gesehen am 02.10.2025 
520 |a We develop precise geometric descriptions of the conjugacy class [x] and coconjugation set C(x,x')={y∈W̄|yxy−1=x'} for all elements x,x' of any affine Coxeter group W̄. The centralizer of x in ̄W is the special case C(x,x). The key structure in our description of the conjugacy class [x] is the mod-set ModW̄(w)=(w−I)R∨, where w is the finite part of x and R∨ is the coroot lattice. The set C(x,x') is then described by ModW̄(w') together with the fix-set of w', where w' is the finite part of x'. For any element w of the associated finite Weyl group W, the mod-set of w is contained in the classical move-set Mov(w)=Im(w−I). We prove that the rank of ModW̄(w) equals the dimension of Mov(w) and investigate type-by-type the surprisingly subtle structure of Mod W̄(w). 
650 4 |a centralizer 
650 4 |a conjugation 
650 4 |a crystallographic group 
650 4 |a e Coxeter group 
650 4 |a Reflection group 
700 1 |a Schwer, Petra  |d 1979-  |e VerfasserIn  |0 (DE-588)1154819779  |0 (DE-627)1016189370  |0 (DE-576)50125885X  |4 aut 
700 1 |a Thomas, Anne  |e VerfasserIn  |0 (DE-588)1160892237  |0 (DE-627)1024283631  |0 (DE-576)506219917  |4 aut 
773 0 8 |i Enthalten in  |t International journal of algebra and computation  |d Singapore [u.a.] : World Scient. Publ., 1991  |g 35(2025), 03, Seite 403-465  |h Online-Ressource  |w (DE-627)324469276  |w (DE-600)2028773-2  |w (DE-576)105430633  |x 0218-1967  |7 nnas  |a The geometry of conjugation in affine Coxeter groups 
773 1 8 |g volume:35  |g year:2025  |g number:03  |g pages:403-465  |g extent:63  |a The geometry of conjugation in affine Coxeter groups 
856 4 0 |u https://doi.org/10.1142/S0218196725500109  |x Verlag  |x Resolving-System  |z lizenzpflichtig  |3 Volltext 
856 4 0 |u https://www.worldscientific.com/doi/10.1142/S0218196725500109  |x Verlag  |z lizenzpflichtig  |3 Volltext 
951 |a AR 
992 |a 20251002 
993 |a Article 
994 |a 2025 
998 |g 1154819779  |a Schwer, Petra  |m 1154819779:Schwer, Petra  |d 110000  |d 110400  |e 110000PS1154819779  |e 110400PS1154819779  |k 0/110000/  |k 1/110000/110400/  |p 2 
999 |a KXP-PPN1937633896  |e 4779985277 
BIB |a Y 
SER |a journal 
JSO |a {"name":{"displayForm":["Elizabeth Milićević, Petra Schwer, and Anne Thomas"]},"origin":[{"dateIssuedDisp":"2025","dateIssuedKey":"2025"}],"id":{"doi":["10.1142/S0218196725500109"],"eki":["1937633896"]},"physDesc":[{"extent":"63 S."}],"relHost":[{"title":[{"title":"International journal of algebra and computation","subtitle":"IJAC","title_sort":"International journal of algebra and computation"}],"part":{"year":"2025","pages":"403-465","issue":"03","text":"35(2025), 03, Seite 403-465","volume":"35","extent":"63"},"titleAlt":[{"title":"IJAC"}],"pubHistory":["1.1991 -"],"recId":"324469276","language":["eng"],"disp":"The geometry of conjugation in affine Coxeter groupsInternational journal of algebra and computation","note":["Gesehen am 16.05.2020"],"type":{"media":"Online-Ressource","bibl":"periodical"},"id":{"issn":["0218-1967"],"zdb":["2028773-2"],"eki":["324469276"]},"origin":[{"publisherPlace":"Singapore [u.a.]","dateIssuedKey":"1991","publisher":"World Scient. Publ.","dateIssuedDisp":"1991-"}],"physDesc":[{"extent":"Online-Ressource"}]}],"person":[{"family":"Milićević","given":"Elizabeth","roleDisplay":"VerfasserIn","display":"Milićević, Elizabeth","role":"aut"},{"role":"aut","display":"Schwer, Petra","roleDisplay":"VerfasserIn","given":"Petra","family":"Schwer"},{"family":"Thomas","given":"Anne","roleDisplay":"VerfasserIn","display":"Thomas, Anne","role":"aut"}],"title":[{"title":"The geometry of conjugation in affine Coxeter groups","title_sort":"geometry of conjugation in affine Coxeter groups"}],"type":{"media":"Online-Ressource","bibl":"article-journal"},"note":["Gesehen am 02.10.2025"],"language":["eng"],"recId":"1937633896"} 
SRT |a MILICEVICEGEOMETRYOF2025 

Ähnliche Einträge