Arthur's Invariant Trace Formula and Comparison of Inner Forms

THIS MONOGRAPH PROVIDES AN ACCESSIBLE AND COMPREHENSIVE INTRODUCTION TO JAMES ARTHUR’S INVARIANT TRACE FORMULA, A CRUCIAL TOOL IN THE THEORY OF AUTOMORPHIC REPRESENTATIONS. &NBSP;IT SYNTHESIZES TWO DECADES OF ARTHUR’S RESEARCH AND WRITING INTO ONE VOLUME, TREATING A HIGHLY DETAILED AND OFTEN DIFFICULT SUBJECT IN A CLEARER AND MORE UNIFORM MANNER WITHOUT SACRIFICING ANY TECHNICAL DETAILS.&NBSP;<DIV><BR>THE BOOK BEGINS WITH A BRIEF OVERVIEW OF ARTHUR’S WORK AND A PROOF OF THE CORRESPONDENCE BETWEEN GL(<I>N</I>) AND ITS INNER FORMS IN GENERAL. &NBSP;SUBSEQUENT CHAPTERS DEVELOP THE INVARIANT TRACE FORMULA IN A FORM FIT FOR APPLICATIONS, STARTING WITH ARTHUR’S PROOF OF THE BASIC, NON-INVARIANT TRACE FORMULA, FOLLOWED BY A STUDY OF THE NON-INVARIANCE OF THE TERMS IN THE BASIC TRACE FORMULA, AND, FINALLY, AN IN-DEPTH LOOK AT THE DEVELOPMENT OF THE INVARIANT FORMULA. &NBSP;THE FINAL CHAPTER ILLUSTRATES THE USE OF THE FORMULA BY COMPARING IT FOR <I>G’</I> = GL(<I>N</I>) AND ITS INNER FORM <I>G&LT; AND FOR FUNCTIONS WITH MATCHING ORBITAL INTEGRALS.<BR><I><BR></I></I></DIV><DIV><I><I>ARTHUR’S INVARIANT TRACE FORMULA AND COMPARISON OF INNER FORMS</I> WILL APPEAL TO ADVANCED GRADUATE STUDENTS, RESEARCHERS, AND OTHERS INTERESTED IN AUTOMORPHIC FORMS AND TRACE FORMULAE. &NBSP;ADDITIONALLY, IT CAN BE USED AS A SUPPLEMENTAL TEXT IN GRADUATE COURSES ON REPRESENTATION THEORY.<BR></I></DIV>