Methoden Zur Theorie der Ternaren Formen

to E. Study's "Methoden zur Theorie der ternären Formen" Study's "Ternary Fonns" presents a view of classieal invariant theory that remains little known to this day, and that deserves attentive reading. When the book was published, the combinato­ rial investigations of Gordan and of the English school were in their heyday. Hilbert's sweeping finiteness results were not yet available, and the term "algebraie geometry" had yet to take hold. Study's goals were geometrie rather than...
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to E. Study's "Methoden zur Theorie der ternären Formen" Study's "Ternary Fonns" presents a view of classieal invariant theory that remains little known to this day, and that deserves attentive reading. When the book was published, the combinato­ rial investigations of Gordan and of the English school were in their heyday. Hilbert's sweeping finiteness results were not yet available, and the term "algebraie geometry" had yet to take hold. Study's goals were geometrie rather than algebraie. He viewed the symbolic method as an algebraic machinery for the description of geometrie properties, and his style of proof, eoneeptual to the ut­ most, invariably follows a background of geometrie motivation, whieh unfortunately the author seldom reveals. Like almost everyone in his time, Study either ignored or dis­ believed the work of Hermann Grassmann, to whom he pays per­ funetory respeet in a couple of footnotes. The book would have benefited, especially in § 19, from the notation of exterior algebra such as is common today. As it is, the author is forced to produce no less than three three-dimensional generalizations of the original Clebsch-Gordan expansion; nowadays these can be viewed as vari­ ants of one straightening algorithm going baek to Capelli-Young. Study's book breaks naturally into three parts, which can be read independently, onee one has mastered the unusual notation. As a Leitfaden, we summarize the main caveats to the reader.