000121373 001__ 121373 000121373 005__ 20230126110108.0 000121373 0247_ $$2doi$$a10.1016/j.nuclphysb.2016.08.008 000121373 0248_ $$2sideral$$a131017 000121373 037__ $$aART-2016-131017 000121373 041__ $$aeng 000121373 100__ $$aDíaz, Pablo 000121373 245__ $$aCounting paths with Schur transitions 000121373 260__ $$c2016 000121373 5060_ $$aAccess copy available to the general public$$fUnrestricted 000121373 5203_ $$aIn this work we explore the structure of the branching graph of the unitary group using Schur transitions. We find that these transitions suggest a new combinatorial expression for counting paths in the branching graph. This formula, which is valid for any rank of the unitary group, reproduces known asymptotic results. We proceed to establish the general validity of this expression by a formal proof. The form of this equation strongly hints towards a quantum generalization. Thus, we introduce a notion of quantum relative dimension and subject it to the appropriate consistency tests. This new quantity finds its natural environment in the context of RCFTs and fractional statistics; where the already established notion of quantum dimension has proven to be of great physical importance. 000121373 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000121373 590__ $$a3.678$$b2016 000121373 591__ $$aPHYSICS, PARTICLES & FIELDS$$b10 / 29 = 0.345$$c2016$$dQ2$$eT2 000121373 592__ $$a2.21$$b2016 000121373 593__ $$aNuclear and High Energy Physics$$c2016$$dQ1 000121373 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000121373 700__ $$aKemp, Garreth 000121373 700__ $$aVéliz-Osorio, Alvaro 000121373 773__ $$g911 (2016), 295-317$$pNucl. phys., B$$tNUCLEAR PHYSICS B$$x0550-3213 000121373 8564_ $$s483169$$uhttps://zaguan.unizar.es/record/121373/files/texto_completo.pdf$$yVersión publicada 000121373 8564_ $$s1314436$$uhttps://zaguan.unizar.es/record/121373/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000121373 909CO $$ooai:zaguan.unizar.es:121373$$particulos$$pdriver 000121373 951__ $$a2023-01-26-09:30:11 000121373 980__ $$aARTICLE