Giải BGG của các biểu diễn bất khả quy của các nhóm tuyến tính tổng quát GLc(n)

THE BGG RESOLUTIONS OF IRREDUCIBLE REPRESENTATIONS OF THE GENERAL<br /> LINEAR GROUP<br /> <br /> GLn (C)<br /> Nguyen Thi Phuong Dung<br /> <br /> Banking Academy<br /> Tãm t¾t:<br /> Ph©n lo¹i c¸c biÓu diÔn bÊt kh¶ qui cña nhãm tuyÕn tÝnh tæng qu¸t<br /> <br /> GLC (n) ®· hoµn toµn ®uîc gi¶i quyÕt.<br /> <br /> Trong ®ã ®Æc trung cña c¸c biÓu diÔn cã c«ng thøc m« t¶ rÊt ®Ñp ®Ï th«ng qua ®Þnh thuc cña c¸c ten s¬ ®èi<br /> <br /> Si<br /> <br /> xøng<br /> <br /> cña kh«ng gian vÐc t¬<br /> <br /> V<br /> <br /> cè ®Þnh. Môc ®Ých bµi b¸o nµy lµ miªu t¶ cô thÓ viÖc x©y dùng phuc, mµ<br /> <br /> th«ng qua ®Æc trung Eueler - Poincare cña phøc khíp nµy, ta m« t¶ ®uîc c«ng thøc ®Þnh thøc tæng qu¸t cña c¸c<br /> <br /> GLn (C).<br /> <br /> biÓu diÔn bÊt kh¶ qui cña<br /> <br /> Tõ khãa:<br /> <br /> Gi¶i BGG, §Æc trung Eucler - Poincare, nhãm tuyÕn tÝnh tæng qu¸t, biÓu diÔn bÊt kh¶ qui, biÓu<br /> <br /> diÔn ®a thøc.<br /> <br /> 1 Introduction<br /> Let<br /> <br /> Vλ<br /> <br /> be the irreducible polynomial representation of<br /> <br /> T ⊆ GLn (C)<br /> <br /> relative to the maximal torus<br /> with<br /> <br /> the<br /> <br /> character<br /> <br /> GLn (C)<br /> <br /> ,<br /> <br /> of<br /> <br /> T<br /> <br /> .<br /> <br /> In<br /> <br /> the<br /> <br /> Grothendieck<br /> <br /> Vλ<br /> <br /> the equivalence class of<br /> <br /> symmetric<br /> <br /> powers<br /> <br /> Sr (V )<br /> <br /> of<br /> <br /> the<br /> <br /> [Vλ ]<br /> <br /> identity. Explicity, the class<br /> <br /> can<br /> <br /> GLn (C)<br /> <br /> ring<br /> <br /> of<br /> <br /> the<br /> <br /> be expressed as<br /> <br /> standard<br /> <br /> representation<br /> <br /> is the determinant of the<br /> <br /> [Sλi −i+j (V )]<br /> <br /> , keeping in mind that<br /> <br /> λ = (λ1 , λ2 , · · · , λn )<br /> Z ⊆n<br /> <br /> of highest weigh<br /> <br /> of diagonal matrix, under the usual identification of<br /> <br /> S0 (V ) = C<br /> <br /> and that<br /> <br /> caterogy<br /> <br /> of<br /> <br /> polynomial<br /> <br /> a polynomial<br /> <br /> V = Cn<br /> n×n<br /> Sr (V ) = 0<br /> <br /> of<br /> <br /> in the<br /> <br /> classes of<br /> <br /> GLn (C)<br /> (i, j)<br /> r