УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÔØÖ¿ºÃÅÄÐÖ<strong>×</strong><br />
I ÓÒÒ<strong>×</strong>ÄÐÖg(A)ÒÖØÝØÒÖØÓÖ<strong>×</strong>e i¸f i¸Òh <strong>×</strong>Ø<strong>×</strong>ÝÒØÓÐÐÓÛÒÓÒØÓÒ<strong>×</strong>ÓÖi, j ∈<br />
´¿º¿µ<br />
ÒØÖÓÓØ<strong>×</strong>º(i)<strong>×</strong>Ý<strong>×</strong>ÐÐØÒØÖ<strong>×</strong>ÓØÖØÒÑØÖÜÖÒØÖ<strong>×</strong>¸Û<strong>×</strong><strong>×</strong>ÝØÓ ÑÓØÚØÓÒ¸<strong>×</strong>ÓÐØÙ<strong>×</strong>ÓÒ<strong>×</strong>ÖÛØÓØÕÙØÓÒ<strong>×</strong>ÓÚ<strong>×</strong>Ý<strong>×</strong>ÓÙØØÄÐÖ ÌÓÚÕÙØÓÒ<strong>×</strong>ÑÝ<strong>×</strong>ÑÐØØÐ<strong>×</strong>ØÖÒÛÒÔÖ<strong>×</strong>ÒØÛØÓÙØØÒ<strong>×</strong><strong>×</strong>ÖÝ<br />
[e i , e j ] = [f i , f j ] = 0A (e i ) 1−a ij<br />
e j = (f ) 1−a ij<br />
f j = 0 ÓÖi j .<br />
ÛÝØÓ´µº(ii)<strong>×</strong>Ù<strong>×</strong>ØØÓÓÓÒÚÒÒØÒÓÖÑÐÞØÓÒÓÒÓÓ<strong>×</strong><strong>×</strong>ÓÖØÒÒÖ<br />
〈α,α〉<strong>×</strong>ÒÒØÖ¸ÛÓ<strong>×</strong>Ò<strong>×</strong><strong>×</strong>Ó<strong>×</strong>ÐÐØ<br />
ÖØ<strong>×</strong>Ø<strong>×</strong>ÝÑÑØÖÝÓØ<strong>×</strong>ÐÖÔÖÓÙØÒÖÓÓØ<strong>×</strong>ÔºÓÖØÑÒÒÓÓÒØÓÒ(iv)¸ ÓÒ<strong>×</strong>ÖØÓÐÐÓÛÒÓÒØÓÒ<strong>×</strong>ØØÓÒÒ<strong>×</strong>ÓÛÓÒØÒÒÖÔÖÓÙØ<strong>×</strong>ÓÖÒÝØÛÓÖÓÓØ<strong>×</strong><br />
ÙÒÖ<strong>×</strong>ØÒÛÒÓØØØØÕÙÒØØÝ2 〈α,β〉<br />
ÔÖÓÙØÛÐ<strong>×</strong>ÓÓ<strong>×</strong>ÐÐØÛÝØÓØÖÔÖ<strong>×</strong>ÒØØÓÒ<strong>×</strong>Ósl(2, C)ºÓÒØÓÒ(iii)<br />
αÒβ<br />
ÆÓÛ¸Ø<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÛÖÒ<strong>×</strong>ØÓ<strong>×</strong>ÔÓ<strong>×</strong>ØÚÖÓÓØ<strong>×</strong>ÛÛÖÒÓÑÔÓ<strong>×</strong>Ð¸Ò 0¸<br />
´¿º¿µÖÒÓÛÒ<strong>×</strong>ØÚÐÐݹËÖÖÖÐØÓÒ<strong>×</strong>ºÏÖÐÖÒÒÖÐ<strong>×</strong>ѹ<br />
0º<br />
<strong>×</strong>ÑÔÐÄÐÖ<strong>×</strong><strong>×</strong>ÓÒ<strong>×</strong>ÛÖÓØÒ<strong>×</strong>ÖØ<strong>×</strong>ÙÑ<strong>×</strong>Ó<strong>×</strong>ÑÔÐÄÐÖ<strong>×</strong>¸Ò ÌÖØÒÑØÖܸA¸ÙÒÕÙÐÝÒ<strong>×</strong>ØÄÐÖÛÛÐÐg(A)ºÌÖÐØÓÒ<strong>×</strong> ÒØÖÒÓÒÝØÛÓ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong><strong>×</strong>ÒÚÖÖÓÓظÒ<strong>×</strong>ÓØÓÐÐÓÛ<strong>×</strong>ØØ(α<br />
Ð<strong>×</strong>ÓØÖÓÙØÖÃÐÐÒÓÖѺÌÚÐÐݹËÖÖÖÐØÓÒ<strong>×</strong>ÒÒ<strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄ<br />
i , α j ) ≤<br />
ÒÒØÑØÖÜÐÑÒØ<strong>×</strong>a ÐÖÖÚÖÝÙ<strong>×</strong>ÙÐÖÓÑØÔÓÒØÓÚÛÓÓÙÖÒÐÑÓÖÙØÒØÓÒÒع<br />
ij ≤<br />
Ä<strong>×</strong>ÙÔÖÐÖ<strong>×</strong><strong>×</strong>ÛÛÐÐ<strong>×</strong>ÛÒÛÒÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong><strong>×</strong>ÓÖØÐݺ ÑÒ<strong>×</strong>ÓÒÐÄÐÖ<strong>×</strong>ºÁØ<strong>×</strong>Ø<strong>×</strong>ÓÒØÓÒÛÓ<strong>×</strong>ÒÖÐÞØÓÒ<strong>×</strong>Ø<strong>×</strong>ÑÔÐ<strong>×</strong>ØÛÝØÓ ÑÓÚÖÓÑÒعÑÒ<strong>×</strong>ÓÒÐÓÑÔÐÜ<strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄÐÖ<strong>×</strong>ØÓÒÒعÑÒ<strong>×</strong>ÓÒÐÃÅ ÄØÙ<strong>×</strong>ÐÓÓØØÒØÖ<strong>×</strong>ÓØÖØÒÑØÖÜÑÓÖÐÓ<strong>×</strong>ÐݸÒ<strong>×</strong>ÛØÛÒ<strong>×</strong>Ý<br />
)¸ÒÙ<strong>×</strong>Ò(ii)Û ÓÙØØѺÖ<strong>×</strong>ظÝØØÖÒÐÒÕÙÐØÝ(α i , α j ) 2 ≤ (α i , α i )(α j , α<br />
<br />
j<br />
[h i , h j ] = 0 ; [e i , f j ] = δ ij h j ;<br />
[h i , e j ] = a ij e j ; [h i , f j ] = −a ij f j ;<br />
i<br />
ij<br />
= 0<br />
≠<br />
i¸ÓÖi={1, 2, . . ., r}¸<br />
´¿º¿µ<br />
(α, β) > 0 ⇒ α − β ∈ L<br />
(α, β) < 0 ⇒ α + β ∈ L .
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