caa a22 4500 445320397 CHVBK 20180317142702.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s00023-011-0095-2 doi (NATIONALLICENCE)springer-10.1007/s00023-011-0095-2 Tanimoto Yoh Dipartimento di Matematica, Università di Roma "Tor Vergata”, Via della Ricerca Scientifica, 1, 00133, Rome, Italy aut Ground State Representations of Loop Algebras [Elektronische Daten] [Yoh Tanimoto] Let $${\mathfrak{g}}$$ be a simple Lie algebra, $${L\mathfrak{g}}$$ be the loop algebra of $${\mathfrak{g}}$$. Fixing a point in S 1 and identifying the real line with the punctured circle, we consider the subalgebra $${\fancyscript{S}\mathfrak{g}}$$ of $${L\mathfrak{g}}$$ of rapidly decreasing elements on $${\mathbb{R}}$$. We classify the translation-invariant 2-cocycles on $${\fancyscript{S}\mathfrak{g}}$$. We show that the ground state representation of $${\fancyscript{S}\mathfrak{g}}$$ is unique for each cocycle. These ground states correspond precisely to the vacuum representations of $${L\mathfrak{g}}$$. Springer Basel AG, 2011 Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/4(2011-05-01), 805-827 1424-0637 12:4<805 2011 12 23 https://doi.org/10.1007/s00023-011-0095-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-011-0095-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Tanimoto Yoh Dipartimento di Matematica, Università di Roma "Tor Vergata”, Via della Ricerca Scientifica, 1, 00133, Rome, Italy aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/4(2011-05-01), 805-827 1424-0637 12:4<805 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer