The Exponential Nature and Positivity |
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Authors: | Hans Plesner Jakobsen Hechun Zhang |
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Institution: | (1) Institute of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark;(2) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, PR China |
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Abstract: | In the present article, a basis of the coordinate algebra of the multi-parameter quantized matrix is constructed by using an elementary method due to Lusztig. The construction depends heavily on an anti-automorphism, the bar action. The exponential nature of the bar action is derived which provides an inductive way to compute the basis elements. By embedding the basis into the dual basis of Lusztig's canonical basis of , the positivity properties of the basis as well as the positivity properties of the canonical basis of the modified quantum enveloping algebra of type , which has been conjectured by Lusztig, are proved.Presented by A. Verschoren. |
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Keywords: | dual canonical basis bar involution exponential operators positivity |
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